OK. I think I have solved the problem.
I am now getting 13.5 volts at the connection on the Power Converter (where I was getting 1.5 volts previously).
After reading all the advice you guys posted, I started looking into those areas you pointed out.
I had replaced the connector on the back of the truck so I know that is good.
I also cleaned and tested the end of tow cable on the TM - so I know that is good.
While troubleshooting this issue this weekend I also opened all the wire nuts in the refrigerator compartment on the side of the TM.
They were all in good shape - no corrosion etc (I replaced all wire nuts here a few years ago anyway).
So then I started looking at all the ground points on the Avalanche.
I found a broken ground strap between the hood and the firewall - I cleaned and repaired it.
Cleaned the ends of the ground cable from the engine block to firewall.
The underside of the truck is very rusty, so I located all the ground points I could find - about four in all.
I used PB Blaster on all ground points then I removed the bolts and scrubbed everything with a wire brush, then I reconnected them.
After that I began to look for ground points under the TM.
The only connection that looked suspect was one of the gray water tank probes - it was rusty and corroded.
I disconnected it and scrubbed it with a wire brush and replaced.
That was it.
I left the TM battery disconnected, plugged in the Tow Cable and started the truck.
Put the meter on the positive and negative block on the Converter and to my surprise it now reads 13.5 volts!
I reconnected the TM Battery and tested again - 13.5 volts and holding.
In addition, I managed to fix another important issue while investigating all this.
I found that the power lead to the safety breakaway cable for the brakes had been severed at one point along the frame!
Not sure how that happened, perhaps it has been like that since I bought it, but in any event I reconnected the line so all is well.
I suppose I should test it. Another day....
Thank you to everyone who helped out with advice. It is much appreciated.
Our next trip is in August to the Thousand Island region in upstate NY - about a 4-5 hour trip.
I will post here the results of running the fridge and cooler.
Hopefully it goes well.
~ John