I concur (I always wanted to say that) with 64fleetside. Bad ground. Check it at the place most people check last. The tail light housing.

Take the tail light housings out of the fenders completely. Get some sandpaper and clean all the area where the taillight assembly screws to the fender. Find some star washers to use under the screws. A little dialectric grease at that point of contact won't hurt.