The clutch does use a relay that will be located in the underhood fuse and relay panel (called the PDC). Look at the under-cover road map of the panel to find the location, then swap that relay for another one just like it (there will be several). If the A/C now works... but the thing you swapped it with does not... it pretty much condemns the relay, which is pretty cheap compared to a compressor clutch.
If you're not feeling any magnetism on your clutch when you request A/C operation and relay swapping doesn't help, you could try jumpering the circuit manually inside the PDC. Terminals 30 and 87 will be power in and power out to the clutch, with the terminal numbering cast into the base of the relay. The two terminals will be across from each other and they'll be the two that point different directions.
If it still won't engage, check your circuit resistance between terminal 87 and ground. Terminal 87 is the output circuit to the clutch and the clutch is normally grounded, so expect to see resistance of around 10 ohms or a bit less if OK. The specs say that the clutch coil shouldn't be less than 4 ohms, in which case it's shorted internally, but you have half-a-mile of wiring you're also testing, so resistance will be a bit higher.
And then there's the whole controls thing. The clutch relay is commanded on by the engine controller (PCM), which in turn gets its urge to fire from the A/C controls inside the truck. To be sure that the compressor relay is being requested to fire, you'd need to look inside the PCM's head with a scan tool ... to see what it sees.
In addition (you knew there had to be more), the daisy chain of switches used to protect the refrigeration system have to be aligned and OK before the PCM will allow the compressor to turn on. You have a low-pressure and a high-pressure cutout switch that are wired in series in a sense circuit to the PCM. The switches are normally closed and switch electrically open if they detect the fault they're designed to. So, testing for each switch is to just put a jumper wire/ paper clip into the socket to complete the circuit. If the low pressure switch is preventing compressor operation (and the system is filled properly), jumpering the low pressure switch will complete the signal circuit and allow compressor operation. Same for the high pressure switch in case the switch believes the system is overcharged. So, yeah... it does get a little involved.
As for the pressure switches, they'll be mounted in the high and low pressure lines. Look for a 2-wire switch, then jumper it and test your compressor for operation. Replace the one that was preventing the system from running and that should do it.