Total shot in the dark:
I remember that on a Ford car and a Ford pickup I owned long ago that there was a part called the "neutral start switch" that kept the car from starting unless the transmission was in neutral or park. It also turned on the backup lights when in reverse. Assuming there is something like that on a 1988 model Toyota, it could either get out of adjustment or go out and prevent the backup lights from coming on.
It was located on the side of the transmission near the place where the gear selector connected.
Again, never having worked on a 1988 4Runner, I can't give anything better.