You are correct in most of your thinking. Which is a good thing. I hate it when I'm confused or puzzled, don't you?
The magnetic coil has two leads. The one in question could have been grounded right at the mount for the coil itself as long as the compressor is grounded.
That is where the rub comes in. Some other users of the coil/clutch may rubber mount items.
Some run both wires into a harness. Example is lawn mower cutting decks. The PTO use configuration varies wildly.
So instead of hanging out a loop of wire to know where. It is tucked or run to look more professionally built.
The more expensive the car, the more they hide what should be the easy stuff. I love those special clips, plugged, taped or labeled over screws. That's a Humble Opinion or a fact. Take your pick.
All in all, it is more likely that you are not get power to the coil or the coils wires have opened internally.
Check the resistance of the coil with a ohm meter. Check from the green lead to the mounting point of the coil on the compressor.
If it shows continutity, check power wire from the harness.
This power will come through the low pressure switch on the top of the aluminium accumulator over by the firewall on the passenger side. That switch can be checked for closure the same way as a coil.
While you have the connector off the switch. You can check for power to ground on one side and then across it back to the compressor coil with a the voltmeter. This will check the all the wiring over while comfirming other control operation.
Some people just jump the connector. If your running the engine when you are out of refrigerant, then you dry run the compressor. This can pull the system into a vacumm. If you have a leak problem, then moisture can get in.
Some can hear it click with the engine off or even see it pull in. Your choice on all that.
Post back if you are not cooling. Some of us need the entertainment,
Phil
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