Not possible as suggested. People will game the system.
When it comes to pregnancy and childbirth, there are many a danger to both mothers and children. Yet that hasn't stopped people trying to "game" it and try to get something more out of it for millennia.
Other answers suggest some sort of rationality from people at large yet even in our world we have had parents try to get benefit from their progeny. Sometimes it's real, like The Great Stork Derby from the early 20th century but that's one of the few cases where the parents had a tangible benefit in front of them.
There are many folk beliefs and practices that have no basis in reality whatsoever, yet mothers subject themselves and their unborn for supposed benefit:
- some milder variants are just fortune reading or horoscopes. They don't require anything from the parent and child and are shown to be completely unreliable. Yet the practice continues to this day and is quite popular. In some (admittedly rare) cases, a potential parent will try to "influence" the fate of their child by trying to bring it on a specific date, so perhaps they would be born under a different sign or otherwise will get a different fortune reading.
- speaking of trying to bring children on specific times - there have been a lot of cases of this over the years. It doesn't have to be tied to fortune reading - some parents would try to bring their children on a specific holiday (so, the child might be blessed or protected in some way) or perhaps avoid some supposedly bad days (when it would be cursed in some way). And there are many other reasons to assign special meaning to a birth date. Again, there is nothing tangible or real behind this yet parents have been trying to force a birth despite this.
- some folk beliefs aren't that much about the birth itself but might assign special meaning to actions the mother does during the pregnancy. These include practices supposed to grant the child some benefit (beauty, strength, intelligence, courage, luck, etc.) or avoid some potential harm (laziness, cowardice, stupidity, ugliness, misfortune, etc.). Yet again, there is no actual link between the practice and the supposed quality it would give or avoid, yet parents have and do practice these. So milder variations might have the mother do or avoid doing something that's ultimately of no consequence. But some practices might involve the mother imbibe poisonous, toxic, or otherwise dangerous substances. Or even harm herself and/or the baby physically. Some of the practices are not very pretty and luckily are mostly left in the past, yet even today there are home made pregnancy tests and even tests for the sex of the baby...
- ...home made anything related to pregnancy has the potential to be harmful. These home made recipes are still widely practised today but have their roots in ages past. Most of these have reliability less than 50% - pregnancy tests, tests for the sex of the baby, recipes that are supposed to help the mother or the child, recipes supposed to protect, etc. The sort of common thing between them is that they require mostly everyday stuff. Maybe bleach which can be highly dangerous, maybe some salt which isn't. Some foods might be preferred or avoided which, at best, has no relevance, but might deprive the mother and/or child of valuable nutrients.
So, for ages people have tried to influence the pregnancy and birth to result in some benefit, even when they can't or actually harm the mother and/or child. If there is any real benefit to be had, they'd intensify their efforts.
At the very least, you can expect more pregnancies and births. So, perhaps you can see a lot of polygyny relationships where one man has many women as spouses, so if at least one gives birth to a child at the right time, the whole family benefits. If we take this a step further, it could be applied to a whole community - if at least one child in the village is born at the right time, it would be of great boon to the whole village, as their protector. So, the village can only benefit of many pregnancies.
This...could turn dark. So here is the thing - pregnancy and birth are a potential problem to the woman. Even today there are many dangers. Not sure the exact state of medicine in your world but I'd expect there to still be dangers. So, of the father cares about the (future) mother, they won't take the decision to have a baby lightly. I'd avoid most of the details, but let's say that if the father didn't care about the (future) mother, they would be free to take the decision to have a baby together. The woman doesn't exactly need to have a choice in the matter. Men can take concubines to have children with and then just "adopt" the right child into their own family. The concubines could be slaves. Or worse.
So, overall, people will be trying to get a powerful child as it's a real benefit to themselves, their family, and their community. That is despite the potential problems the birth can pose to the mother. Thus, the system where everybody has a shot at getting a powerful child, instead of that being a lucky occurrence, cannot work.
There is a way to preserve the overall idea but...
You have to change the system
The major problem is that everyone has a shot at giving birth to a powerful witch. And since the parameters are known (or can at least be guessed quite easily) then everybody can plan and act accordingly.
Here is some things you can do to make the powerful witch child a lucky occurence:
Drop the solar eclipse requirement. Make it unpredictable
The problem is that it's too easy to aim for it. Even if there is no way to predict the correct time 9 months in advance, if it's calculable at any length of time, people will try to aim for it. Just try to space out the conceptions in a community within about a week of each other and you're set - there would be at least a few mothers that will be ready to give birth about every week, so whenever the even arrives, they'd try to induce an early birth.
So, it has to be completely unpredictable. Perhaps not until something like 5-10 minute window. That way, nobody will be able to plan and try to induce an early birth. It it might not even be a global event but something highly localised in some fashion. That way, even if people from city A don't get a powerful witch baby, they wouldn't be able to know that people from city B had the opportunity to get one.
In fact, it might be best if nobody is even aware that the baby is a powerful witch at birth. Because a rival city or family might try to kidnap the baby at the very least. So, it's better if only later does their power manifest. At least around 6-8 years old would be good enough to make it feel special and lucky.
People will still try to get advantage for their children. You cannot stop that - again, just look at the real world. However, if their efforts don't work, that would limit the risk they expose the mother and the baby to.
Limit the pool of powerful witches
This could be an interesting way to keep the "lucky" element and keep the time of birth being predictable. Simply limit how many powerful witches can there be in the entire world.
As an example, in Avatar: the Last Airbender and the successor show Legend of Korra there is a single Avatar in the entire world. Once they die, a new one is born. This is heavily based on the Dalai Lama as the Avatar is partly a spiritual leader who reincarnates. At any rate, it's one way to make the "limited amount of witches available" - once one dies, they reincarnate. Or perhaps there is a different reason for the limit - maybe even unknown. It could be as weird as "there is only one per constellation and no more".
If you keep the celestial event requirement, then they can only reincarnate (or whatever the justification is for the limit) at that that point in time.
You can restrict on how many powerful witches can there be - only one, like in Avatar, or perhaps 100 or 10 000. Depends on how you want the story to go but you simply cannot have more than that number in the entire world. Or maybe there are very special requirement to join the ranks of the powerful witches and increase their number permanently. At any rate, even if one gives birth exactly on time, there is no guarantee that the child will have the powers of a powerful witch.
Do note, that this can put the witches at more risk. After all, if no more can be born now, then a simple solution is to kill one and plan a birth at the next significant celestial event. You can have quite good chances of success, then.
Make the powerful witch highly dangerous
This can make the powerful witches feel special but in a completely different way. Simply having them might be bad news. They might lack morals, or lack restraints, or be highly volatile. Or any other thing to make them incredibly dangerous. In that case, having a powerful witch child might be more of a curse than a blessing.
Here are some possibilities
The powerful witch can produce powerful magic but...not always what you want. Not always what even the witch wants.
- The magnitude of the spell they cast might be off - lighting a campfire and burning down the forest are both possibilities when they try to produce a flame.
- The effect might be unintended. Even if the witch wants to produce flame and can get the correct amount, perhaps sometimes they get a flock of birds in addition or instead. There can be all sorts of things that show up you don't want.
- The witch can manifest effects despite their wants or needs. They might need to work hard at controlling themselves to not randomly summon a lightning bolt or maybe there is no controlling that. Of particular problem might be times the witch is not in any control, for example when sleeping.
- The magic the powerful witch casts might be bound to very specific restrictions. Perhaps they cannot affect cold iron or anybody wearing it. Or people born on a Tuesday. Or other weird characteristics would come into play. So, while this might be reliably always the case, it's not going to be easy trying to determine the limits. Also, the conditions might switch. For extra fun (well, from out of world perspective) the powerful witch might get new sets of restrictions and rules for their magic instead of experiencing high and low tides. So, in effect, their magic might be powerful but would seem quite random from the outside. And they might not even be able to completely figure out the rules by the time a new switch comes in.
- The powerful witch itself might be rebellious and would simply despise following any rules or guidance. They would be unruly to such an extent that they won't be a boon to their community. Not for very long, at least.
This is different to the above. Instead of the powerful witch being sort of random, they would be consistent...but ultimately not very useful:
- The powerful witch has exceptional magical talents at their disposal. However, instead of being a boon to their community with their spells, the witch is lost within the world of magic. Daydreaming, fantasising, absent-minded, lost within the world of magic. It's exceptionally hard to make them focus on the real world and harder still to keep their attention there enough to ask them to do something for you.
- the powerful witch might be bound by different rules of magic permanently. So, even if they cast the same spell as a "normal" witch, they'd get a different effect. The difference in this scenario could be that it's not random...but it's still sufficiently different that it makes learning and using magic much harder. Imagine if there is a brilliant mathematician but for them calculating 2+2 always yields 5. A triangle for them will also somehow have two sides. The rules just don't work the same as for anybody else. So, they can still be of benefit but it's hard to work together and especially hard to get a specific effect.
- The witch just cannot understand others. Either cannot relate, or tends to misinterpret, or literally is unable to comprehend communication. It makes the powerful witch exceptionally hard to deal with.
As an example, the tabletop game Mage: the Ascension has the widderslainte. These are mages who followed a dark path in a past life and managed to permanently taint themselves and essentially turn to evil magic. Once they reincarnate, they don't remember any of this but are still evil and uncontrollable psychopaths even as normal mortals before the Awaken (read: become mages). Once they do, any magic they cast is evil and twisted. In the Mage cosmology, the source of magic is sort of separate from the human who wields it. So, it's in theory possible for the human to be redeemed (but exceptionally hard), yet they cannot cast anything but magic that is corrupt and brings harm and ruin to the world. Even killing a widderslainte doesn't help much as they would just reincarnate and you'd have to face them again.
So, working with "widderslainte"-like idea - perhaps the powerful witches are also unable to do anything but harm. So, having one in your community is probably bad. If they not only wield "bad magic" but are also bad people, you definitely don't want them around your family or your community. Just imagine a bunch of little Damiens from The Omen.
This has to actually be counter-balanced in some fashion because of the powerful witches are so undesirable, people will steer way clear from giving birth to more and can even just kill the child young or even the mother than let one loose in the world.