In a 2003 Ranger the PCM(computer) activates AC compressor when it gets "AC demand" signal(12v) from the dash switch/selector
PCM will not activate or will turn off AC if coolant temp exceeds 240deg(approx.) or throttle shows WOT(wide open)
But I doubt either of those are the issue
In the engine fuse box is the AC Clutch relay, that's what the PCM activates, you can swap it out with similar relay in fuse box, not PCM or fuel pump relays, lol
I would unplug the AC clutch wires and put a volt meter on them
Start engine and activate AC, should see 13.5-14.8volts, engine/alternator running voltage
If so, plug wires in to clutch, it should activate, if not then yes, field coil is failing or has too big of an "air gap"
If voltage is 0(under 1volt) then PCM is not activating the AC relay, could be a Pressure switch is failing, and engine bay needs to heat up enough to close the switch, "freon" pressure changes with Heat, a failing pressure switch "might" be out of spec
You can test each pressure switch, engine cold, to see if either is open, if so change that switch, no you don't have to drain "freon", the pressure switches on all AC systems are "hot swappable"
If voltage at clutch connector is low, under 10volts, then could be corroded wires at AC relay base or at fuse 25
Test voltage at AC relay base, key OFF, should read Battery Voltage exactly, there are 5 slots, only one will read 12v with key off, that's from fuse 25, test voltage at fuse 25