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Based on the tests you have done, if all were done correct then you have confirmed the PCM is not receiving the AC request signal or the PCM is faulty and not sending the command to the clutch relay. If you need the circuit diagram, to check your work, let me know.
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Auto or manual AC?
Sedan or coupe?
Below are the links I will be using.
Based ion the tests you have done its the ECM or the multiplex. Do you have access to a diagnostic tool to see if either of those are getting the AC request signal, resulting in not grounding the clutch relay pin 4?
The multi meter can only verify the relay is not getting a ground command via OHM testing but it does not have the ability to see if the modules are getting and receiving signals. We know its not sending a signal out since the relay is not closing.
Neither fan relays or the clutch relay appear to be getting the ground on pin 4, which is why none are activating. We just need to know if the multiplex is telling the ECM you want the AC on.
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You can not test a communication wire for power or ground. Its a signal it sends not a power or ground. Its like comcast in your home. One wire brings you 1000 channels, 100 gigabytes of internet and phone, and there are hundreds of other homes all on that same one single wire.
You need a diagnostic tool. A test light and multi meter can test a relay which you have already done. When you jump the pins 1 and 3, your bypassing the relay and the modules.
I have no clue what a relay circuit tester is. I have never heard of that tool nor seen one. The diagnostic tool is called a HDS diagnostic tool.