Oo, oo, I have an answer to this one. I had the same problem in the shower of our Carver 32, dark as a cave in there, so I mounted one of these -
...believe it or not a Coleman under-the-lid ice chest light. It's designed to turn on automatically when you lift the lid, but that knob in the center turns off that feature. That knob also functions as a simple on/off. Great thing is that it's battery powered, no wiring runs, no switches, sticks to any surface, and it's waterproof, designed to live in coolers with melting ice. Plenty bright for a shower, and the batteries lasted at least two years (we sold the boat before they died). That was the easiest, fastest boat improvement I ever did.