well the compressor cycles on when the pressure sensor on the high side of the system sends a signal that the pressure has dropped and the compressor needs to kick on to get the pressure back where it needs to be.
That said, there are several things to check here.
My first thing to check is to rotate the compressor wheel with the engine off and key out. It’s possible that the clutch got too hot or something and is actually sticking together so the clutch never actually disengages.
The next thing I would do is hook up some gauges and make sure that the pressures are where they need to be.
If the pressures are good, then the next area I would look at is the high side pressure sensor. With the engine running and the a/c on, use a multimeter to see if the sensor is sending a constant “on” signal to the control module.
If the sensor is acting normally then it’s time to start hunting down a short in the system. Get your wiring diagrams out and work from the compressor back. If not then just replace the sensor, although I’ve never actually seen a pressure sensor malfunction and actually make the compressor constantly run.