But it does seem to turn off the alarm, at least for the first 2 seconds or so, then the temp goes out (normal). after that first start up alarm, the switch being on or off doesn't seem to matter.
Unless I misunderstand all what you are saying here, how would you know that being on or off doesn't matter unless you experienced an over heated engine and then tested the switch to see if it mattered? Sounds to me like you have been lucky.
Water temp is the difficult sensor to test. You would need to put it in hot water measured with a thermometer. Oil pressure is easy: it should be silent while running, but sound when the engine is shut down. If your alarm is silent after your engine is shut down, then you have been lucky, so far.
If you have mechanical gauges, not quite so serious, but idiot lights and especially alarms are very helpful.