One hint, the reverse light seems susceptible to taking in some water. My reverse light has been out for a while and I've just changed it today. I found that water has got into the connection between the bulb and the contact, and when I replaced with a new
bulb it wouldn't work. The problem was that the metal contact wasn't touching the bulb so I got some pliers and pulled the contact further out. When I put the bulb in again it touched the contact and would work fine. This may not be what's up with your reverse light, but it's worth a shot anyway.
Robert, October 2007