Ok... if you follow that large suction line back to the compressor, is there a 2 wire switch at all?Also about the 2 wire plug, my accumulator doesn't have it. Unless I'm really overlooking something.
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This system may not use the clutch cycling method like the 2006 and prior models do if there is no switch.
Your setup may be like that. So in this case, there are some other ways that GM uses to control it.
Some compressors have a control valve inside the compressor to keep the pressure above the freezing point.
Others use a sensor located inside the evaporator housing to monitor temperatures and when they get below freezing it will then cycle the compressor off. Yours is probably some form of this method
We need to figure out which one you have. Might need a scan tool that can access the HVAC module to see things further. I know you said you have manual Controls, but now a days its still computer controlled LOL!!
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