so a few days back on my US 1997 xj6L the AC stopped cooling, i tought it was gas cause the car had been parked for over 6 months. but today i took it to AC garage and they told me it was full of gas but the compressor wasnt turning on. so i told them to not do anything that this is something i can prolly fix myself if its electrical.

just want to know if there is a common cause for the AC compressor to not turn on so i can start looking there.

Check fuses.
Check wiring to compressor and clutch
Does clutch engage?
Check trinary switch
Run a/c module self test sequences

I have the same issues with my 1995. Which fuses (of the never-ending collection of fuse panels) do I check?

The clutch is not engaging. I think it is one of the electrical connections. There is one on the compressor that is similar to a fuel injection connector. I've popped it on and off a couple times the compressor clutch doesn't engage.

I have a test noid light for fuel injectors, I wonder if the same test light would work with that connector.

Are there any other connectors near the compressor that we just can't easily notice?

The most likely reason for the clutch to not engage is low refrigerant pressure. Test by jumping the sensor.

Where is the sensor?

in my case the pressure was good. can you elaborate more on jumping the sensor.

ahh traced the problem to another corroded connection but this time it was a harness connector near the AC compressor a big one was corroded and had a broken leg so had to do a jumper and AC working again.
on this connector.