Ok... more research.
First, I have the factory manual on my computer. Took myself to dinner a few nights ago and spent a couple hours staring at all the pages to see what I could see.
The trailer taillight circuit blows its fuse whenever the headlight switch is on. I forgot to check if it blows without a trailer or other load (have a plug-in tester) attached, but don't think so.
The taillight circuit is very simple and runs from the power distribution box to the rear of the truck with only two connectors.
The symptoms tell me this is a short but we have checked the wiring harness and find no evidence of changes after it left the factory.
The wiring has been fine up until a month or so ago.
I plugged in a voltmeter in place of the fuse and it is showing 12 volts, but there is still no output at the rear of the truck.
Any suggestions/ideas?
I am not terribly excited about unwrapping the entire length of the harness to find the problem, but with only 2 connectors, I think that is what I am going to have to do.