Why does my Mother keep her eyes closed so much of the time?

Good point. In fact, my spouse has macular degeneration in one eye and he has installed LED lights all over the house. I have have had sensitive eyes my whole life, and always needed sunglasses. I can't stand LED lights. They hurt my eyes terribly and I walk around turning them out once he has left the room (because, of course he leaves them on!) Sometimes I feel like I am living inside a refrigerator.
Could it be your mother has a lot of floaters in her eyes? If she does, bright lighting makes it even worse - its like ghosts floating before your eyes, and if she has dementia, it could be really upsetting.

Betsy, my parents had to get glasses that would automatically change to darker lenses any time they were in a bright light, otherwise they would be sitting with their eyes closed.

I believe as we all start to age, the sunlight or too much indoor lights becomes very sensitive to our eyes. My sig other always needs to wear sunglasses when he is outdoors.

Makes sense what Babalou said. Could it be she has "dry eye" from medication and her eyes burn but she can't tell you why she is uncomfortable?

My mom did this when she started taking gabapentin (Lyrica). They had to discontinue it.