Paul:If the socket hanging down has 1 wire going to it, it has to be grounded for the light to work. Have you checked all the bulbs? It's possible they are all burned out. Don't laugh, I have seen it when I worked on cars professionally. They would go out one at a time, and suddenly when the last one goes out, people realize they don't have dash lights. I think the radio light is wired through the rheostat, so that would indicate the rheostat is working. Unless someone has changed the wiring in the radio, like I did my T-Bird.
John