You may be getting a tiny bit of voltage feedback due to grounds between vehicles. As old biscuit is eluding to it could be in the umbilical or the connections on the trailer.
I would open both ends of the umbilical if it is a jumper and clean and tighten. The same with every connections associated with the tow lights
Are you traveling with running lights on? Do you have a charge line?
Any minute amount of voltage sneaking back onto the brake light circuit even though not enough to light things up could cause it to shut off.
Even check the electric brake grounds.
