Ok...those 2 fittings are the high and low side to the system. That compression fitting is where the orifice tube is for the front AC system.
Btw..your connections look normal with that black rubber stopper in there. Thats normal and what GM uses from factory.
2nd...lets address why your clutch wont come on.
When you have the lit snowflake the hvac control head sends a signal thru the BCM to the PCM requesting AC operation. The PCM is in complete control of the ac clutch.
There are 2 safeties are in this circuit.
There is obviously the one on the accumulator.
There is another and it might be on the backside of the compressor itself. Thats the high pressure cut out. Both these will keep the clutch off if theres a problem.
Easy peasy test. Unplug both sensors and let the truck be off for about 5 mins. Ohm them. They BOTH should be closed when the system is at rest. If they are closed, then you need to do voltage testing to see where you do and dont have power: fuse, relay, etc.
If the high pressure one is stuck open, its bad replace it. If the low pressure one is open, stop, you have a refrigeration charge issue and need that addressed. Carefully check your wiring around the compressor. And make sure you didnt break a connection going to the high pressure cut out
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