This is for a 1998, I assume that the VCM provides ground for the relay, allowing voltage to the compressor clutch. A4 at the relay is hot with ignition on.
I'm pretty sure you can jump the cycling switch (on the accumulator) to see if the compressor kicks on. Temporarily, of course, in case it is a good part and legitimately shutting off the compressor due to refrigerant issues. The switch is maybe $5, and is on a schrader valve so it can be swapped out with minimal refrigerant loss.
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