I think I found it, and it explains my inconsistent test results from the low-pressure switch all the way around to the clutch. I pulled the EATC and when I apply 12V to the EATC's clutch output (Purple) everything engages consistently. After a hint in my Google searches, I dismantled the EATC and there was a shot solder connection on the mainboard relay "normally on" pin. Very clear. I touched it up and so far the AC is working, but the post I found that led me there also said his solder fix lasted for 3 days before it went bad again, suspecting a partial internal short in the clutch itself causing the system to draw enough amps to melt that solder point. So now I want to figure out the right way to test around the entire path for any shorts just to be safe.