That 10ga wire is your main chassis power. It powers pretty much everything that isn't connected directly to the engine. However, keep in mind the bulkhead connector diagram posted before is a modified '84-'86 diagram. Yours may be (probably is) slightly different.
What I was trying to say before was that you need to check which wire is delivering power to the light itself (at the tail light end). After passing through the main chassis electrical wire to the bulkhead connector power runs several different routes to get to the tail light (via the brake switch, the turn signal switch, the light switch, and the reverse switch). You need to determine which one is at fault (the wires are color coded). My guess would be that there is a fault in the the reverse switch (mounted on the transmission).
According to the wiring diagram for '81-'83 posted by Jeephammer
the three colors should be:
White = Tail Lamp/Brake Light
Light Green w/ or w/o Trace = Turn Signal
White w/ Trace = Backup Lamps