[BB_TX]

You are correct that the gas and the electric are electrically independent of each other, with one exception and that is the inside switch panel which is 12 vdc to both switches. The 12 vdc switch for the electric side energizes a relay at the water heater that in turn sends 120 vac to the heating element. See the diagram below. Possibly there is a bad/loose wire connection to that panel. They also use a common 12 v ground at the water heater junction box that could also have a bad connection.

You might also check the two thermostat/hi temp cutouts that they are tight against the tank. Some have reported in the past that one or the other was not tight and subsequently not controlling the temp correctly. The thermostat/hi temp cutout device has two functions. It is a thermostat controlling the temperature. And it is a hard cutout for too high of a temperature and requires a manual reset via the pushbutton on it.