I haven't had this happen, but, could be a grounding issue. especially if you're running a new painted or aluminum shank on your truck. It should have a wired ground, but, that may be compromised and seems to be the most likely place to start if all of the lights are working normally. My dad has a trailer with a grounding issue that will come and go when traveling down the road. I wouldn't recommend his fix, but, he drilled a threaded hole in his receiver and has a bolt that keeps constant tension on the shank so that the whole system stays grounded through the truck. It's an 18' utility trailer, I probably would have just re-wired it if it were mine since it's not a complicated setup.
I have a buddy that bought a used boat and had a similar issue. It was also a ground and he fixed it in the trailer wiring.
None of that may help you, but, since no one else chimed in, I thought it may give you a place to look on the trailer first.