This may sound silly, but has anyone ever hung a mirror over a door?

I don't think that would add any light to the entry way, usually you add the mirror on the opposite wall to reflect light back into the room from the source (your side lights). or if you have a wall on the left or right of the door that might add some light. https://www.huffingtonpost.com/entry/10-design-tips-to-brighten-a-dark-hallway_us_580a86e5e4b0b1bd89fdb24e

You could also add wall sconces or if there is an entry way console table, put a small lamp on it and a large mirror over it. https://www.google.com/search?q=pictures+of+entry+console+table+with+lamp+and+mirror&client=opera&hs=lU1&tbm=isch&tbo=u&source=univ&sa=X&ved=2ahUKEwibkuO7yorbAhUBzGMKHYwwBSEQsAR6BAgBEFE&biw=1326&bih=658

Even adding bright LED night lights if there are plugs helps. https://www.amazon.com/Pack-SnapPower-Guidelight-Batteries-Installs/dp/B0727Z2VV2

This is your main entry. I can’t imagine the difficulties of adding that kind of weight to your hinges, and how you would secure it well enough (clunk clunk every time the door opens) to keep it from falling off without damaging the door itself. Besides, mirrors would only reflect your Hall. I

You could have someone cut out the two small top panels and put in glass on the door. Or four top panels and put in attractive glass for light.

Or just put handsome large mirrors on the walls on either side of the door. Now they would reflect light

Use Command Velcro hanging strips on the mirror and it would not bounce around with the movement of the door.

Sharon is right. I don't think it would reflect enough light where there is no light to reflect.

The place to reflect the light that somes in through your sidelights is on the adjoining walls

I too would put it on one of the side walls.

I put one on an interior hollow door with a hole in it. I used the 2-sided adhesive squares, and it did not work, because of the "give" in the door. I had to glue the backer behind the mirror, to the door. I took it off its hinges and let everything dry horizontally, with books on the mirror, to ensure it was making contact everywhere with the door.

I’ve always had my mirror on my door. Never an Entry way . Right now I have one on my bedroom door.

I use the flat metal over the door hangars.

Then I use the command strips on the bottom To keep the mirror from bouncing back and forth.