I believe your headed in the right direction. I believe the ref voltage to
the temp sensor goes hot, with the key on. On a warm engine, the gage
should give a reading. You can check for ref voltage. You can do an ohms
test across the sensor terminals, that is the terminals on the sensor not
the wiring connector.

You could probably use a proper resistor across the connector terminals,
just for testing purposes, and the vehicle should start and run, if the
sensor was the problem. I wouldn't let the engine run for very long with
the sensor disconnected, for all kinds of reasons.