We finally resolved the issue on Friday, and my suspicions about the vehicle were correct. It did turn out to be the power adapter that was bad, although I practically had to drag the mechanic under the car to check it out. He saw where a wire had sorted out on my son-in-law's trailer a year earlier and tried to blame the problem on that.
Anyway, turns out that the my neighbor (and campingva) were both right, the newer cars use thinner wire because (duh) most of the lights are LED and don't require thicker gauges. So the shop had correctly installed a power adapter that taps directly into the 12V system, and then tapped into that for the trailer lights. But that adapter only worked intermittently with the tail light feed...when I tested it was fine, but it wouldn't hold.
Anyway, all is working fine, thanks for all the input, and hopefully this will help someone in the future who encounters the same thing.