[rotorwrench]

Either unit can be tested in a pan of water with a hot plate using an Ohms meter on the two terminal unit to see if it opens the bimetallic switch at high temp or rig the single terminal unit with a long jumper to the gauge wire to see if it gets a temperature reading that compares to another thermometer in the heated water. The single terminal unit's body needs a common ground with the battery but the two terminal is just a temperature sensitive switch. It's either open or closed to current flow depending on the temperature it's exposed to.

It sounds to me like there is an intermittent open circuit there when you start. If the circuit is open or the switch is off the gauge indicates hot.