Hello I will help you with your question,
You have done most of the testing but I would be looking at the ERLS fuse in the instrument panel fuse block.
This fuse supplies power to the coil side of the relay, you checked the power side by jumping across the #30 to the #87 pins of the relay socket?
Use a test light if you have one to check for power to the relay
Let me know what you find and I will work with you from there
Do you have power to both of the relay pin cavities? There are two sides to this relay and two fuses. The ERLS fuse supplies power to the coil and the AXC fuse which supplies power to the compressor so two pins of the relay will have power with the key in the run position
Let me know
OK here is the location of the AC fuse and the AC relay
Save this picture for future refrence
The AC switch sends the AC request to the PCM and the PCM grounds the AC relay to turn the compressor on. Put the clip lead of your test light on the positive terminal of the battery and the tip on one of the non hot terminals with the engine running, the relay out and the AC on so that the fans run. See if you have ground at one of the non hot terminals. Unplug the compressor before you start the engine.
Let me know if you have ground at one of the terminals
Is this a testlight or what kind of tester?
You said you had three hot (powered) pin cavities in the relay block?
There are four or five pins on the relay you have?
You should have two that have power with the engine running and the AC selected on. One of the others will be the compressor so if you were to use a large paperclip to jump from one of the hot terminals to the compressor terminal the compressor would run. If you look on the relay you will see #30 and #87 or #3 and #5. Connecting these two is what the relay does when you press the AC switch
The other terminals ( #85 and #86) are the power and the ground that is supplied by the PCM and this tells the relay to connect the #87 to the #30 and the compressor turns on.
I need you to find if one of the terminals is grounded with the engine running, the AC selected on and the compressor un plugged.
You are missing a contact. There have to be 4 so you will have to disassemble the box and repair the contact. It may have been pushed down into the box.
This is the removal procedure, you will have to remove all the fuses and relays to release the plastic clips on the sides of the box and seperate it. Work slowly I do not have diagrams for the disassembly of the fuseblock.
If you are unsure about this repair you may want to replace the entire fuseblock. You can find used parts in your area at car-part.com
Let me know what I can do to help you with this
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Thanks for accepting my help
I am curious about what you find so please let me know once you have had time to swap the boxes or have repaired the original box
No need to reply until you know or unless you have further questions about this