Well, today I had the Tekonsha Prodigy P2 brake controller installed; the installer gave me credit for the Curt unit they had originally installed. I told the technician that I had a problem with the right turn signal and, half an hour later, he told me that he had found and fixed the problem: a dirty connection that he cleaned up with WD-40. I really hope he's correct; I should get to test the trailer lights this weekend though I won't be able to give the controller a test until I return from a trip.
So, let's hope he found the problem; thanks to all for your ideas!
Gary,
Elgin, TX