I had an 84 that had this same problem... I'm sure that it is a ground related problem, but I never was able to track it down.
I went as far as to pull then entire body harness out of the car and checked it over thorougly. I was unable to locate anything that would have caused this.
Rather than put the original harness back into the car, I chose to find an 84 in a local wrecking yard to put back into my car. This did solve the problem, but was rather extreme.
On the bright side, I probably had the nicest wired Supra on the road.
Anyway... Good luck and I hope that you have better luck finding it than I did.