Sir, THAT is a problem! The MAXIMUM allowed voltage drop on any power circuit is 0.5V on the power side and 0.25V on the ground side - all measured from BATTERY GROUND on the power vehicle.
So, if you measure the voltage at the receptacle on the truck with the cord off (open circuit) and get 12.5V, the LOWEST acceptable voltage at the wheel end of the brake power wire is 12.0v, anything less indicates a serious wiring issue - high circuit resistance.
You also need to measure the voltage on the GROUND wire/frame with all lights on and some trailer bakes applied to assure you don't get more than 0.25V showing, if you do get more then there is a grounding problem.
All the talk about having to measure amps, resistance etc is hogwash, although knowing the amps is handy few people have a meter that can handle direct readings of more than 10 amps and therefore it is not possible to do. And no, inductive meters are NOT good enough, but they can give you a relative idea of the amps.