This "green switch" is the coolant temperature sensor for the fuel injection and the ignition module. It's actually two sensors in parallel. There is a resistance from each pin to ground, that varies with coolant temperature. It's quite important to the fuel injection, as you discovered. New sensors are readily available. And highly recommended.

The other two similar looking sensors run the dashboard gauge (single pin) and the electric fans (four pin).

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Norm in NJ
Next oil change at 230,000miles