That pigtail switch has nothing to do with comp cut-out. It's function is solely for the Aux Fan Low speed cut-in if high side pressures demand more airflow......nothing more.

The sw. that cuts out comp is the other one. [ spade connector one] . That is a binary sw and cuts in at 2 bar for low refrig monitoring and cuts out at 30 Bar for comp protection.

The circuit that is suspect is the blue sensor/thermistor in the water jacket. That is engine coolant temp input to the ACC panel and it's function is to cut in the high fan, @ 105C, but it also has a higher temp cut-out value to cut compressor signal if engine is heat soaked or extremely HIGH.
Next time, before start-up, look at the CT indicator on dash.
If high reading, that is the suspect.
If not , then you need gauges on the high side before start for further diagnosis..............

__________________
A Dalton