I haven't heard of the Mustangs having this same problem, but there is a sure-fire way to tell. The constant control relay module is in the passenger inner fenderwell. Pin# 23 is a black/yellow wire that goes from the A/C clutch relay (located inside the CCRM) to the A/C clutch field coil. If you have power at pin 23 on the CCRM, you should also have power on the black/yellow wire on the A/C clutch connector.
FYI, the black wire on the A/C clutch goes to ground.
I don't think the Mustang harness is routed nearly the same as the Explorer. The PCM sends a ground signal through pin 69 to the CCRM's pin 22 that grounds the A/C clutch relay coil and clicks on the AC clutch relay, which powers up that black/yellow wire coming out of pin 23.
So that's how the PCM turns on the A/C clutch... it sends ground to the AC clutch relay coil. There are conditions that have to be met in order for the PCM to allow this clutch to engage. The AC controls have to be set to norm a/c, max a/c, mix, or defrost. The A/C clutch cycling pressure switch has to be on (refrigerant pressure has to be correct), and the AC high pressure cutout switch has to be open.
Typically, the reason AC clutches are not commanded on by the PCM is that the AC refrigerant pressure is too low, normally due to a leak. But it could be pressure is too high, or that one of the switches is bad. Normal procedure here is to temporarily bypass the A/C clutch cycling switch to see if the A/C suddenly kicks on when you do. If it does, then you know that's your problem... either the switch is bad (unlikely) or the pressure is too low due to a leak (likely).