turn on your emergency flashers and check the lights this usually overrides everything if the flashers work, it may be in the switch if not, check the bulb, socket, and the connectors
sorrry , didn't read the whole post befor I replied sounds like a bad connection somewhere or an intermittant or medium resistance short. if it was the rear mounted battery, you would have melted cables or severe arcing which would be east to see
I think your battery is shorted internally and check your grounds from the engine to the chassis and from chassis to engine block. change the battery and try again
On my 67 Dart, the left brake light only works when the right turn signal is on. I have a chassis wireing diagram, but not for the column. I can read schematics and I know thats where the problem is and think I know why. ( rusty ground caused over current). Fixed the bad ground but its time...