ECM replacement?

You should take the relay out, turn the A/C on and put your meter across pin 86, the ECM pin and battery negative. With the car on. This will voltage drop that ground circuit while it's hot. If you read anything besides very close to 0. There's a ground issue or the ECM driver for that ground is having problems. You're correct though you may have an ac pressure sensor issue. It's a 3 wire sensor on the A/C line. It should have a 5 volt reference, a ground, and the pressure signal wire. But there's so much involved in this HVAC system. The BCM, HVAC control module, inside air temperature sensors, ECM, and the ambient temperature sensor on the front grill near the radiator.
It might be in your best interest to have a full system scan done. It might show a diagnostic trouble code in the HVAC system and give you some better direction on this diagnosis.

Take it to AutoZone or advanced auto and have them scan the system for trouble codes. They don't charge anything. If there's any codes write them down and we can go from there. I mean the onstar system is tied into the HVAC system as well. This is a complicated unit. I'd hate to see you testing every part, you'd be at this forever. Let me know when you're done with work and I'll have you check a few other things. One more thing, is the radio showing the outside ambient temperature?

You had the car scanned for codes already? Every module? And is it about 84 where you are? I'm just asking because if the ambient temperature sensor fails, it stops reading on the display. Have you tried swapping the relay with another? I'm assuming you have.

Just asking because relays have a coil in them. What I need you to do is take the relay out and put your meter set on voltage, from pin 86 to a good ground and turn the A/C on so the ECM grounds that pin. Going to battery negative would be best but I know that will be difficult since it's in the trunk. So find a good ground on the frame. It should read close to zero. This is voltage dropping that circuit. We need to know if there's a drop in that circuit while it's active with the key on. Just don't stuff the meter leads in the relay pin, just touch it, you don't want to spread those relay pins.

Okay good, nice to have someone who knows what he's doing. Definitely something seriously wrong there. I'm looking at actual Cadillac wiring diagrams now, and I'm still concerned about those pins being backwards. Has anyone done any work to this before? I've looked in 3 different places and pin 30 is where the power should be coming from, not 87. And 86 to ground should be 0volts. I don't know why you're getting reversed voltages like you are. I'm wondering if someone replaced that fuse box and wired it wrong or something. The voltage drop on that control wire is 3.2 volts. Cause the 3.2+10.4 is your battery voltage in full.

Can you pull a fan relay and see if pin 30 is battery power on that one? Because all the other relays are the same. The only relay that's different is the Fan S/P relay. But that's getting power from fan relay 1 for different fan speeds.

I guess the relay can be a reversed relay, but the voltage drop of 3.2v isn't right. Does the compressor relay have 4 or 5 pins?

Well 85 and 86 can be reversed, the relay would still work. I just think there's got to be a corroded wire or connector causing that 3.2v drop to the ECM. Which is why I think when you're driving you have the ac coming and going. Road and engine vibrations can causing a connection to made then broken. I'd find that dark green/white wire coming out of the fuse box and trace the wire looking for a connection issue. Unless the ECM is having a pin issue. But the voltage drop is the issue. The maximum voltage drop you should have is.050v. I don't see any connections on that wire between the ECM and relay. That's why I was wondering if under the fuse box there was corrosion. If not try tracing the wire.

Well, you're going to have to check that wire at the ECM, with the way the compressor is coming and going, there's got to be something loose or corroded. The compressor wouldn't come on at all if it was an open circuit. Check contact points on the wire harness around the engine and the 3 ECM grounds on the engine block. You have to get rid of that 3.2v drop. That's what you're chasing here. Just don't unplug the ECM with the key on and remember that a pin hole in a wire can cause corrosion inside the insolation. There isn't much I can do not being at the vehicle. I'd trace that wire all the way to the ECM. That's what you're going to have to do if you want to fix this yourself. I've had to take wire harnesses apart to find tiny corroded spots. Go to the ECM and see if you get that drop. And have you checked the actual plug on the compressor too. The compressor grounds to the engine block. Think of how that ground works, it goes from the relay to the ECM, then the ECM grounds to the engine block. I've gone through these wiring diagrams for 3 days now. Have to check at the ECM. If it grounds fully there, then you need to work your way back.

This is what Technicians go through everyday. Chasing wires and bad modules. It's not an easy job.