I gotta ask: has any work been done one either the truck or trailer since the last time it worked correctly?
As stated by others, the only way brakes can be applied is to have power on the brake apply pin. First suspect to me is always review previous work. Only then would I suspect a failure in the wiring. If it is like my Tundra, the tail lights are not on when the key is on, only the front DRL. So, that power source can likely be dismissed. But, if yours, like mine, has the factory tow package there is a battery charge pin for the breakaway battery, or other trailer batteries, it will be hot when key is on. A mis-wiring there would do it.
I also suspect that a breakaway switch failure would put 12v on the source wire as well as the brake apply circuit. I'm not sure how the tech tested that function. But if I were doing it, I'd put a diode in between the breakaway switch and truck power lead and test for voltage on both sides. that would determine if the truck is definitely the culprit.
curious problem! Please let us know the outcome.