Very simple process and you can actually look at the monovalve to see if the gaskets/rubber are damaged or if there are any foreign particles that may have lodged around the seal at the bottom of the valve.
If I remember I think it will also react when it is out of the body so you can see it function.
You are right in that failure equals open all the time or constant heat. When 12 volt is applied it will actually move down in the cap to cause the seal to close off water supply at the bottom.
If you are getting constant 12 volt to the unit then this would indicate that it is trying to close to stop the flow of water into the heater core.

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