If you can't find the light kit, you could replace the whole compass. I seem to remember a lighted version. Or you could go techy and drill holes in your boat, mount a cool little cowled light on deck, run wires, mount switch & battery box, blah blah. My solution is not techy or cool. On the infrequent times I need a compass at night (doing a before dawn crossing, etc.), I duct tape a light stick (I prefer red for this) next to my compass. I put a strip of tape on the light stick so it doesn't shine back in my eyes, only forward onto the compass. So it's not elegant, but it's easy, cheap, works fine, and doesn't malfunction.
Touring Kayak Paddles
Wall Mount Boat Racks