My very similar clutch coil has a static resistance of about 6 Ohms. You can test for that at the relay (system off, engine off...) to determine the health of the coil itself and all the wiring and devices between.
There's a coil ground lead that, at least on my car, is connected to the compressor body at one of the screws for a manifold plate. If that's not connected to ground, you'll see the symptom you describe with 12V on both sides of the pressure switch with key on. The resistance check I described above will identify that missing connection. You can go to the stub cable connector by the compressor, and test for coil resistance to ground there, and if it's way higher than the ~~ 6 ohms I measured on mine, you've localized the open to the clutch coil and its connections.
Of course, my first-diagnostic-step is almost always to go back through the work you've done since it worked last. Things work until they don't, and the mission is to find out what happened or what you did during that time.
Considering the very recent "re-gassed" effort, I'd extend my search to include the reason for that, and if that reason was solved. Old gas leaked out? -All- the leaks fixed? What is the actual pressure in the system? If the pressure switch is no longer held closed by refrigerant, the compressor won't run. Your diagnostic of 12V on both sides of the switch points away from low refrigerant charge as a symptom, but it's still worth checking just to be sure. Replace the switch in the circuit with a jumper, then listen for the clunk of compressor clutch pulling in when AC is selected. No need to start the engine, but key must be in 'run' position (II) to do this test.
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Tom added the pic of the current flow diagram while I was typing. It looks like the G17 AC Relay is there for isolation/suppression of the reverse EMF from the clutch coil when it opens. The diagram also shows that the pressure switch is the last element in the clutch coil feed, after the AC suppressor relay. Your test of battery voltage at both sides of the switch points harder towards Tom's diagnosis of a bad clutch coil. Still, the check for continuity from the black/red at pin 4 in that AC relay socket (relay removed), or from E45 or F15 (still black/red) where it passes through the CE panel. Measure resistance to ground with your DMM, and you should see the coil resistance. Key is off for these tests. If the connections are solid and the clutch coil still shows open, then the coil is the the culprit.
FWIW, these clutch coils are amazingly stout. The suffer when there's a LOT of heat, but you usually see other symptoms of that heat before the clutch fails.
My amateur nickel is telling me the refrigerant has leaked out. To collect the nickel if I'm wrong, send a SASE and I'll drop the nickel in and return it.
