[mjlaupp]

Originally Posted by SirDrake

....Next, I disconnected the Tow Cable from the TM (I opened the side compartment on the TM and untwisted the wire nuts connecting the Tow Cable's positive and negative lines).
With the truck running and plugged into the TM tow cable, the reading at the ends of the cable (bare wires) I get approx 13.5 volts. So voltage is passing through the Tow Cable from the truck no problem.....

13.5 volts is a normal reading with no load on the circuit. Add a load (converter) and you get:

....If I connect the positive cable from the Tow Cable to the positive cable that goes to the on board Power Converter, the reading drops to 1.5 volts!!!.....

You have a bad connection or corrosion on the 12 volt line between the TV battery and the point where you are measuring voltage. Does your Avalanche have a battery isolation device? My first suspect area would be at the 7 pin connector.