Problem with diagnosing problems over the internet is I can not see what is going on.
First question I have to ask is there TWO flashers plugged into the fuse box (or just above it for the flasher). If so do they make a clicking noise when you activate the light in question. Have you checked for blown fuses? (if your rear bumper goes under water; such as fording streams, or driving on city streets when they flood) that blows the fuse. I can think of all kinds of possibilities but I lack information.
I had and still have similar issues. I agree that it is most likely grounding issues. my brake/tail light sockets were not grounding well against the housing. also, there was some issues in my dash with grounds.
also, found out the hard way that you cant use some LEDs especially for blinkers if you have the original flasher. so if you put LEDs in, then they wont blink unless you buy the special flasher