Couple revisions to my setup to address the above two concerns.
First concern was getting +12V to the aux pin of the 7-way trailer connector, so the Prodigy RF would turn on. Before going any further, member ShawnA solved this in a different - and probably better - way than I did here: Tesla stopped supplying 12V power to the aux pin of the 7 way - Fixed!!!
Pulled the rear cover back off and the harness out.
Here's the harness with the tape removed:
And the mapping of wire colors to function in the 7-pin:
The brown, red, and yellow/red wires are all a heavier gauge than the others.
I spent a little time testing voltages, and saw the following against the reference (brown) ground:
Car On, lights off:
Tail lights: 11.6V
Left & right: 11.6V
Aux: 0V
Reverse: 0V
Brakes: 0V
After the change the Aux pin voltage now matched the tail lights voltage, both +11.6V with the lights off.
When turning on the lights (even the parking lights) voltage went up to 13.9 on the tail light and aux pins. Turn signals would bounce up the voltage on the left/right turn pins. Didn't test the reverse pin but wouldn't use it anyway.
When it came time to pair the Prodigy, it initially wouldn't pair with only 11.6V on the aux pin. I had to turn the lights on (was doing this in broad daylight so they wouldn't come on on Auto) - and then it paired. It remained paired even when the lights had been turned back off, so I should be set now. Didn't have time for another test tow but should be doing it again within the next couple weeks.
The other thing I did with it apart was paint the bracketfor the 7-pin black, and reinforce it a bit better on the other side of the panel.
Lower/underside of panel:
Upper side of panel:
All put back together:
