Which motor does your beetle have,Customer
The compressor receives its power from the fan control module via the brown wire with the red tracer. The first step would to check for power on that wire at the A/C compressor clutch. If there's power, with the engine running, A/C on and the compressor inoperative, try gently tapping on the compresor clutch. It is common for the magnet in the clutch system to get weak, or the spacing between the clutch and hub to increase with wear, and eventually widen to the point that the clutch magnet can't pull it into the engaged position.
Check that first, and let me know. If this helped, hit the "accept answer" button, and thank you in advance.
Please do. I will be in and out all day tomorrow, and will look for your input.
As far as I can tell by the wiring diagrams, there is no compressor-clutch specific relay. Its contained in the fan control module. Until I hear from you, I will research that module for possible pattern failures.
Thank you again.