In the 1400AD, there was a temple built to honor a late king somewhere in the middle east. The temple can house a thousand people and have many facilities from amenities to entertainment plus an indoor olympic size swimming pool, only a handful of servants are working in the temple. Is there a good way to automatically lit up these rooms at specific time of the day without supervision? Complement question is how to save energy by automatically turning off the light when the room is unoccupied?
Yes and people have been doing it for millennia.
Only reliable way to tell the time of the day without any maintenance is by the direction of the sun. You will need to time this by the sun being in the correct position.
Conveniently the sun is also a source of light, so you do not need to take care of timing and lighting separately. Simply build your structure so that it has openings that "point" to the correct direction and allow the light in when the sun is in that direction. Personally I'd reflect the light from metal reflectors to the ceiling that is also covered with reflective metal so that the entire ceiling "lights up" when the sun is in the right direction.
Only real downside is that this is much less effective when it is cloudy but as mentioned there really is no reliable maintenance free method to even know if it is the correct time in that case.
If you want the rooms lit when occupied and unlit when empty, the solution is to have the occupants light them.
Create reflective surfaces such that small amounts of light will amplify. Every visitor to the temple is given a torch upon entry. Or a lantern. Some reasonably safe (doesn't make the air unfit to breathe, doesn't start fires easily), easy to carry, long-lasting light-emitting device. A lantern that burns candles or food grade oil is probably best, but I'm answering for the method, not the specific energy source.
When a visitor enters a room, s/he places the light source in the designated location and the reflective surfaces cause the entire room to illuminate. The more visitors in a room, the better the light.
The staff can supplement lighting in rooms without enough people and they don't have to worry about rooms with plenty of people. Or if visitors know they will be in a room without a lot of people, they can take two lanterns/etc.
Is this system automatic? Well, technically yes. The staff don't have to do it and the light increases when people enter the room and decreases when they leave. It's just powered by people (the transportation of the lighting and the placement, not the light itself).
Is there a good way to automatically lit up these rooms at specific time of the day without supervision?
Yes. Line up the floors, walls and ceilings with zync.
Sphalerite ((Zn, Fe)S) is a mineral that is the chief ore of zinc.
The wiki also says this:
Around 95 % of all primary zinc is extracted from sphaleritic ores.
Part of the ore is made of zinc sulfide. Its own page in Wikipedia has this to say about it:
Zinc sulfide, with addition of few ppm of suitable activator, exhibits strong phosphorescence (described by Nikola Tesla in 1893), and is currently used in many applications, from cathode ray tubes through X-ray screens to glow in the dark products. When silver is used as activator, the resulting color is bright blue, with maximum at 450 nanometers. Using manganese yields an orange-red color at around 590 nanometers. Copper gives long-time glow, and it has the familiar greenish glow-in-the-dark. Copper-doped zinc sulfide ("ZnS plus Cu") is used also in electroluminescent panels. It also exhibits phosphorescence due to impurities on illumination with blue or ultraviolet light.
The temple insided will start glowing the moment they stop receiving natural sunlight. The effect may last for hours, depending on the amount of zinc you are able to apply.
Complement question is how to save energy by automatically turning off the light when the room is unoccupied?
With medieval technology? I don't think that's possible.