My method would be:-
1) short the control side of the relay to ground (with the engine running) and confirm that the compressor clutch engages.
2) Test at the relay to see if the ECU is grounding the relay when you push the a/c button.
3) if (2) isn't working, test the wire at pin 13 of the ECU to see if it's being grounded when you push the a/c button.
4) if (3) isn't working, you're now into confirming the inputs to the ECU (pressure and temp sensors, believe you may have already done this?).
Garages have a habit of blaming the ECU when they run out of diagnostic ability. I'm always extremely skeptical when someone tells me that a garage has diagnosed there issue as a failed ECU.
Hopefully in the home stretch for diagnosing. I will confess that electrical terminology is not my forte, so before doing anything too destructive to my ECU, I need a bit more help in clarifying my observations to date. Using my voltmeter and discovery to date.....
1. Shorting the control side of the relay (30/87) engages the AC clutch, compressor, fan = nice cold air.
2. All the inputs to the ECU confirmed functional
3. Constant 12v at connection 30 on the relay
4. Relay connections 85 and 86 become a closed circuit when engine running (14V approx.)
5. Circuit 85 and 86 remains closed when AC button pushed.
So - here’s my question. When I push the AC button, all things working as they should, my understanding is that the electromagnet (low current) is energized (+12V) and causes the AC clutch circuit to close. But the circuit is always closed with the car running. Or… Does the electromagnet switch instead activate when the low voltage circuit opens (85/86 becomes an open circuit).
Sorry if my electrical terms and descriptive are a bit lame - hope you understand my descriptive.