ECM replacement?

Pin 86, the control wire to the ECM has 9volts on it with the relay out? Ahh I had a thought, the reason you have 9.6 volts on pin 86 with your meter going to positive is the ECM is grounding that circuit. It's just not making a good ground which is why this problem is coming and going. You have a bad ground somewhere. The ECM is unable to fully ground the circuit, you need to check both batteries and all the grounds on the car. Or you have a corroded ground going to the engine block. Try running some jumper wires from the engine block to the frame and to the housing of the compressor. See what happens. Make sure they're good solid ground connections. Check the exhaust for any melted wires on it as well. Both sides of the engine.

This is the cts sedan rwd, correct? Can you send the VIN number please.

Here's a different location than All Data:

Here's another picture:

Check behind driver side headlight. I've looked in 4 different places, for whatever reason these ECMs seem to placed in different locations depending on where the vehicle was manufactured. Did you try running some ground wires from the frame to the engine block? This would tell you if there's a bad ground between the two.

That's another location for the ECM, down behind the driver side headlights. Looks like he's going through the wheel well. But you should be able to see it from up top on driver side looking down.

No it won't turn the A/C clutch on unless the cars running. There's no reason to. I think you have a bad ground really. Because of the readings you're getting. If you were on the ECM pin that grounds the relay, and on battery positive with your meter, if you think about it, you're reading positive and ground through the ECM. But with only 9.6v, that tells me something is not grounding correctly. You should be reading full battery power in that case because the ECM is giving you ground. Same way it activates the relay. I am a bit concerned about those power pins for the relay being reversed. That's very odd.