I tried running a ground to the left socket but all it did was make the tail light so bright that it makes it hard to see the turn signal flashing.
This sounds like you have the lights wired wrong. The bright filament should be the brake/turn signal and the dim filament should be tail light.
As several other people have said but you haven't caught on yet, GROUND THE BED TO THE FRAME. GROUND THE CAB TO THE FRAME. GROUND THE ENGINE TO THE FRAME. GROUND THE NEGATIVE TERMINAL OF THE BATTERY TO THE ENGINE.
