Possibly you could make it a triple star system.
If all the stars and planets orbit in almost exactly the same plane the time between the an eclipse of one star by another would be a multiple of several synodic periods.
No matter how you arrange the orbits, there would often be periods when only one star was visible and periods when no star was visible.
If the planet orbited about one single star the star would appear as a sun in its sky during the daytime and would not be seen at night.
And in every year of that planet it would be between its own star and the two farther stars for part of the year and on the other side of its sun for the other part of the year.
At one extreme of the orbit the planet would be exactly between its sun and the other pair of stars. The other two stars would rise when the sun set, and would set when the sun rose.
At the other extreme of the orbit the planet would be exactly on the opposite side of its sun from the other pair of stars, that would thus appear close to its sun in the sky. The other two stars would rise when the sun rose, and would set when the sun set.
And for most of the year the alignment would be in between.
So the natives of the planet would be used to the idea that sometimes the sun and the two other stars would be the sky together, sometimes only the two other stars would be in the sky, sometimes only the sun would be in the sky, and sometimes no sun or double star would be in the sky and it would be dark night. And they would experience all four conditions during the course of the year.
And if the planet has one or more large moons that can be bright in the sky that can complicate matters.
Your idea that it would be vary rare to see only one star in the sky is very naive. Because if two or more stars are seen together in the day sky on one side of the planet, then they can't be seen on the opposite side of the planet when it is night. Many people have tried on these boards to imagine how to make a planet have eternal day on both sides and have failed.
No matter how many stars they add to the system, they can have the planet surrounded by stars on all sides and have eternal day on all sides for periods of years, decades, centuries or millennia. But sooner or later all the orbits of the various stars will put them in the same direction as seen from the planet, and thus there will be night on the side of the planet opposite the stars, perhaps for years, decades, centuries, or millennia.
So the natives of the planet will be used to dark night.
A) Unless there are at least three stars in the system and their orbits are not in the same plane that the planet orbits around its star. Thus the planet would have day and night as it rotated so that each spot faced the star part of the day and faced away from the star part of the day, just like Earth.
Bu the other two stars, farther away, would not heat it up much but might light it up with several times the light of the full moon, for example.
If the other two stars orbited around the center of mass of the system at a right angle to the plane of the planet's orbit around its star, and happened to be at opposite sides of their long orbits for the centuries or millennia of the planet's recent history, they could have illuminated opposite sides of the planet constantly for all of recorded history.
Or there could be only two stars in the system, the star the planet orbits and that gives it day and night and heats it up, and another star that orbits at right angles to the planet's orbital plane and lights one side of the planet, the side where the protagonist's civilization is located, and the other side is unknown and unexplored and nobody knows they have much darker nights there.
And maybe once in a thousand years the planet's moon will eclipse the farther star during the night of the brighter star and bring on true darkness for the first time in a thousand years.
In a different type of system where all the planets and stars orbit in the same plane there could be rare periodic celestial events, periodic eclipses or occultations of the stars in the system..
1) a double eclipse of the farther two stars by the nearer star or sun.
a) One of the farther stars eclipses the other one.
The planet will orbit its star or sun with an orbital period or year, the planet's sun or star and the other two stars will orbit each other around their common center of mass with a second orbital period, and the two other stars will orbit around their common center of mass with a third orbital period.
As the two other stars orbit their common center of mass and the planet orbits its star which orbits around a common center of mass with the two other stars, there will periodically be alignments between the two other stars and the planet so that as seen from the planet one of the two other stars will eclipse or occult the other one.
b) The nearer star or sun eclipses the two farther stars one at a time.
And as the planet orbits its star or sun and its star or sun orbits around the center of mass with the two other stars the sun will periodically eclipse or occult one of the other two stars and then pass into the space between them and then eclipse or occult the other one.
c) Combination of a) and b).
And on rare periodic occasions both events will happen at the same time. One of the two other stars will eclipse or occult the other one while the nearer star or sun will eclipse or occult both of them.
2) the planet's moon (if any) eclipses the near star or sun.
Similarly to the Earth/Moon/Sun in our solar system, the planet's moon (if any) may periodically eclipse or occult the nearer star or sun.
3) Combination of 1) and 2)
At rare periodic intervals the planet, its moon, the nearer star or sun, and the two farther stars may all line up in a line so that one of the two farther stars eclipses or occults the other one while the nearer star or sun eclipses or occults both of them and the moon eclipses or occults all three of the stars.
4) simplified super eclipse.
The situation can be simplified by turning the two farther stars that orbit their common center of mass into one single star. Thus one of the orbital periods can be eliminated.
And on rare periodical occasions the two stars, the moon, and the planet can be aligned so that the near star or sun eclipses the farther star while the moon eclipses them both.
5) Make the planet a double planet or a moon of a much larger giant planet. That way the other planet will appear much larger in the sky of your planet and will have a much better chance of eclipsing the other stars.
Anyway, I think you should have someone else calculate the orbits and orbital periods so that your story is plausible.