Bringing this thread back for a conclusion.
Like others have stated, I was leaning toward a trailer wiring issue. I too, several years ago, had a wire rubbed raw and it was causing problems. But at the same time, one would think that would blow a fuse.
I finally got a chance the other day to start looking around. Took the 7-pin apart and it looked perfect. Crawled under the trailer and looked over all the wiring that was not harnessed. Then starting pulling wheels. The second wheel I pulled, I noticed a wire hanging loose and another wire with a connector on the end hanging loose. They weren't really close to one another but the fact that both were just hanging there and a connector was on one threw up a red flag. So I had my son get in the truck and with 1. nothing, 2. parking lights on, 3. and then with the brakes applied, I would hold the wires together. I figured I'd blow a fuse if it was a problem. Nothing happened.
I stripped the ends, got another connector, and put them back together. The problem has not occurred since. My guess is this was a ground wire and it was giving me intermittent ground. The brakes work better as well and I think that's because I only had brakes on the left side before the break in the wire. But these are both guesses.
Any way, problem solved. Thanks to all.