How do I install an overhead shower light?

There is a junction box there because it is against code to have electrical above the shower.

There are waterproof LED can lights. They look like a full can light, but they only recess a half inch or so. That's what I would recommend

We have 2 of those thin LED lights that are approved for damp places and they work great. Looking closely at your photo, it seems like they put a square peg in a round hole. I believe the fixtures approved for damp locations also have a seal to keep moisture out, which would help reduce air leakage. From memory, check Home Depot and expect to pay $30-35. Before you get too far, make sure that there is power in the box. If not, that may explain no light.

Buy a wet area appropriate fixture, turn off breaker, and twist and screw.

Baz9782607 is right, check for power first. You can pick up a little multitester for about15 bucks. Once you get that figured out, and once you get an appropriate fixture, shut off the power. Hook up the negative, the positive, and the ground. Easy peasy

Call an electrician!! If it’s not done to code it can invalidate your home insurance. It’s not a DIY project. Just because there is a cover there doesn’t mean that proper ground fault wiring is installed.

I find it interesting that it's covered, possibly because it's not to code. I'd check your local electrical building codes before doing anything, then, call a licensed electrician. SAFETY first! Best of luck.

I have non-waterproof aluminum body in my hallway. Mine are only 2" diameter. Here's a photo. I found on Amazon. Check Home Depot, too. We love them and have them all over the place. I'll look for the link to ours. Probably later today.

Hi Brendan, here's the link I promised for my lights. Mine are DC 12v, but you can find different sizes and for 120v AC on Amazon, too. We prefer warm white 2700k-3000k when buying led lights.

Hope this helps!

https://www.amazon.com/acegoo-Recessed-Ceiling-Aluminum-Downlights/dp/B012KCNN5O