This is just a guess, but if when you hear the pump, it makes a kind of machine-gun sound rather than a whir, it is a diaphragm pump, like most RV pumps. This works by throwing a magnet attached to the center of that diaphragm back and forth. If the pump is oriented just right, the bouncing of the rig going down the road could cause the weight of that magnet to bounce up and down just a little bit, so that over the course of a trip, the pressure is built up a wee bit on every bump. I would expect this to happen whether the pump was on or not, and only be prevented by leaving a faucet cracked. Minimal water would be moved, since it does not take much water added to a pipe to run the pressure up. Just a guess, just a guess.