It sounds like a ground problem, I had a similar dilemma on my Samurai. Under the back of my truck, right next to the bumper there were two groups of ground wires (one for each of the rear lights) attached to two screws that threaded up into the bottom of the truck. The problem in my case was that one of the screws, and the ends of the wires attached to it, were so dirty and rusty that they did not conduct electricity anymore, resulting in a whole bunch of weird things going on (brake lights blinking, reverse lights turning only half-way, things would work fine with headlights off but would malfunction when I turned them on or touched the brakes, etc.) I simply cut the ends of those wires, extended them all to the other screw and grounded them there, it solved everything.
I would say this is more likely than what Toynut is suggesting, since a short between two wires would mean that the rubber coating around BOTH wires would have had to rub off in the same place. Possible, but unlikely, and a hell of a lot harder to find, so look for grounding problems first.