I've recently had to move and my new place is fine except i have nowhere in my living room for the cage.

I have a spare room that is large and empty but sadly there is no windows. Even with the door open it's still pretty dark in there. I know they cannot be in the dark all day and night so I was thinking of putting a clip on lamp on the top of their cage and it turning on during the day. I will make sure to use LED's so they don't pose a fire hazard and I won't shine it directly into the cage.

I was contemplating a reptile light fixture but it doesn't seem necessary because I only need it for light so it seems a little bit backwards to spend the extra money for no reason.

Would this be okay? If you were in this situation what would you do?

I would install, most likely in the center of ceiling, something that
would be DAYLIGHT bright. have it on a timer so it's on during the day
and off at night. but I also have a small nightlight on at night so they have just a slight bit of light at night.
When I'm in the room at night I have one small 40 watt bulb in the ceiling
on a dimmer and dim in all the way low, then sit with the gliders and play.