Over the years, I have seen gauges that "float" randomly when the engine is off. Probably nothing to worry about if they work properly when the engine is running.
Some temperature gauges may simply show the present temperature no matter what -- just like the thermometer on the wall of your house. My pyrometer works that way. Right now it shows almost as much as the thermometer on my front porch. I'm not familiar with the pyrometer technology, but there is definitely NO normal 12 Volt wiring involved.
It would be the same with an old-fashioned "mechanical" temperature gauge, where the gauge-tube-and-sender is all in one sealed piece.