Hello: I have been using these small stick up lights to give me some added light on my componets. There called DOT-it lights made by sylvania. Specs on them are 2.5" round and less than 1" thick. They have 3 white leds and run off 3 AAA batteries. Access to them is 3 small screws. They come in several colors, have self stick mounting via 3M tape and last a long time.
I first found these for sale at HomeDepot but its hit or miss per store. I have recently seen them at JoAnns fabric stores. Give them a try they put off no heat and don't need wires or a extra plug in outlet!!!