[consultIII]

If the a/c led is on with the switch engaged the control side is probably ok.

most common reason for no a/c clutch engagement is low refridgerant charge so I would check this first. If high side is below 35psi the bcm will withhold a/c request.

Assuming you don't have gauges to check static pressure.

check for dtc p0530 which will set if pressure is too high or low to operate. View the voltage parameter for the pressure switch if you have a scan tool or measure the voltage at the pressure switch signal wire with a dvom. Need to have between 0.09-4.90 V for the system to work. low voltage means low system pressure and high voltage equals high system pressure. backprobe the red/blk wire at the pressure switch with koeo.
believe the pressure sensor is located on the evap inlet tube near the acuumulator. should be a three wire connector with a gray 5v feed wire. black ground wire and red/blk signal wire.

If the pressure is ok then check your switch.