A/C clutch engagement is controlled by the Powertrain Control Module (PCM). When the A/C-heater control is set to any A/C position, it sends a request signal on the CAN-B bus to the Totally Integrated Power Module (TIPM), which then transfers the request on the CAN-C Bus to the PCM, which determines if operating conditions are correct for A/C clutch engagement. When all operating conditions have been met, the PCM sends a signal on a dedicated hard-wired circuit back to the TIPM to energize the internal A/C clutch high side driver. When energized, the A/C clutch high side driver provides battery current to the A/C clutch field coil.
The pressure switch has three terminals. One is ground, one is a 5V reference, the other is voltage indicating the pressure. If I'm reading the FSM correctly, when everything is working properly you should see 5V on the sensor circuit. You would probably get a check engine fault if there was a short there. You could try disconnecting the sensor and shorting the 5V to the sensor signal wire, the clutch should activate if other conditions are right (like AC is enabled on the HVAC controls). So most likely low pressure (measuring ~0V) or perhaps a TIPM fault, or the transducer failed to the low pressure state.
The compressor inlet should show somewhere between 20 and 50 psi depending on ambient temperature, 25-35 at 80 degrees. Outlet is 200-300 at 80 degrees.