Any automotive relay needs 12volt and a ground to activate, remove either one and relay doesn't activate
Same for a 12volt light bulb, you can give the bulb 12volts on one, or BOTH, terminals and nothing happens
Until you also ground it, no voltage can FLOW THRU the bulb which is what causes it to light up, until it has 12v(positive battery terminal) AND a ground(negative battery terminal)
A Relay needs the same FLOW thru it's "coil" to activate
In your year the AC clutch relay gets 12volts with key on, but has no Ground, so stays off
Pressure switches have 2 contacts inside that are connected unless pressure is too high or too low depending on the switch design
Pressure switch wire is Grounded at one end, then runs from switch to switch so is a GROUND at the other end unless a switch opens, cutting the ground
This Ground is used to activate the AC Clutch relay, which activates the Compressor
If a pressure switch should open AC clutch relay would turn off, saving the compressor from burning out, low pressure, or an AC line from BLOWING OUT if pressure was too high
So a safety thing
In your year Ford put the PCM(engine computer) in the mix, it has an internal relay that connects the pressure switch ground to the AC clutch relay, activating it
So the pressure switch wire runs to the PCM not the AC Clutch relay, and another wire runs from PCM to AC clutch relay's ground
When you select AC on the cab control panel that signal goes to the PCM, and PCM activates it's internal relay, connecting pressure switch ground to AC Clutch relay's ground terminal, since it already has 12volts it activates