I had this situation three years ago. Was very bad and annoying. Never did figure it out during the trip. Then one time while driving at night without a trailer, I noticed my brake lights stayed on for a couple seconds after I released the brake pedal. It was on an 06 dodge cummins. Did some studying and finally figured out that the brakes relied on the power steering system for booster operation and when the power steering fluid got old, the system would slowly return the brake pedal. Drained and flushed the power steering system and filled with fresh fluid and the problem went away.
Hopefully this helps. You might back up close to something and watch your brake light reaction on your TV. This will at least help eliminate your tow rig from the equation.
2014 Eagle 34.5 BHTS FW
2016 Ram 2500 Laramie 4x4 Megacab
4.10 Rearend, bed cam, air suspension