If you want lights that don't also produce heat (which you might, if you have other heat sources dialed in already or if your house is warm enough that you don't want to add more heat to the cage, etc) you can get LED strip lights in a kit with a dimmer. You can set them really dim so that you can just see in, but it's not actually any brighter than a night with a full moon. They're pretty inexpensive. Just exercise a little common sense in how you mount the strip. They generally have adhesive on the back, so you need to either permanently cover or remove the adhesive before attaching them inside some other way, or stick them to the outside of the cage facing in. Don't use the adhesive to stick them to the inside of the cage!!
In any case, they're inexpensive and if you decide you don't like them on your cage you can use them lots of other places.