It sounds like there is a short to the ground or an overload in the circuit. Have you checked the switch? Have you verified that there isn't anything hitting the wire in the center console when moving to reverse? I wonder if someone on here as a diagram of the electrical system and what that fuse is also linked to.
Lol Frumpy, mine were pretty terrible too. I just replaced my Tail Lights with the Spyder ones and when I replaced all of the rear lights I had water sitting inside the plugs. I drained everything, cleaned them out and then greased everything with bulb grease. I live in Phoenix, I never imagined that I would find water sitting in there, but the car does sit in the garage quite a bit too.
If you dont love Muscle Cars your no friend of mine...