I did not know the factory lighting was mounted in the back. That's not a good way to provide light (since the light needs to bounce off the things you're looking at, not backlight them).
I use cheap undercabinet dimmable 12vdc LED strips (maybe 12" long?) I bought off Amazon like 15 years ago, and mount them just behind the top of the door surround. Doesn't take much light, and if they're dimmable you can dial them in.
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