I did some troubleshooting tonight.
First, I swapped the A/C relay for the wiper relay. No change. I tested the connections with the A/C button on and off.
Then, I grabbed my meter. There was no power to the relay on the side with three small posts (the middle one doesn't seem to have a connector to use). One of the bigger two has 14V at idle.
I started probing other switches and sensors after this. Here is what I found:
The connector on the compressor had no power.
The low pressure switch had 14V across it, though I need to retest this. I tried back probing the connector, but the probes were not long enough. So, I pulled the connector and tested across and got 14V. I imagine this will always have power. I will check the switch itself tomorrow.
I tested the high pressure switch, but I forget what I came up with. It's been a long day. I'll check this tomorrow.
The big test tomorrow will be the HVAC control unit. I'll pop it out and see if that button is doing it's job. The light lights up, but I doubt that means anything other than a good circuit for the LED.
I'll also look for a set of HVAC gauges at work tomorrow. I'd like to know what it going on inside the system.