I'm with Doug on the gauge being suspect. The water heater should have little effect on the pressure since the normal air bubble should handle it for the most part. In many years of RV'ing, including about 15 with a pressure gauge on the water system, I've never seen the pressure vary by much more than 4-5 PSI while underway with the pump on. I can't speak for other brands, but the common Shurflo pumps used in many RV's do not use magnets for the pump action. It's purely the mechanical function of a motor driven eccentric cam pressing against several small diaphragms in conjunction with check valves that creates the pumping action. There's no possible way for road vibration to cause the pump to raise the pressure in any meaningful way. Bouncing contacts in a weak pressure switch could conceivably cause the pump to operate momentarily, but in the OP's case, the pump was replaced with no change. Again, the suspicion goes back the gauge.
Dutch
2001 GBM Landau 34' Class A
F53 chassis, Triton V10, TST TPMS
Bigfoot Automatic Leveling System
2011 Toyota RAV4 4WD/Remco pump
ReadyBrute Elite tow bar/Blue Ox baseplate