Troubleshooting mission accomplished
Thanks for all the great advice. I started troubleshooting at the 7-pin connection, then worked backwards.
Turns out I should have started at the back and worked forward, because the problem was easy to see. Every one of the wires that connect to the trailer brakes was ripped out.
I'm guessing I hit a chunk of retread on the road and it went up into the trailer wheels and ripped out the wires.
Now I'm trying to find a schematic so I can re-wire everything, but I'm feeling confident I'll be able to figure it out.
Thanks again ... you guys rock!