Hey PA-Joe: You're onto something. The pushbutton panel inside the car does cycle the compressor on & off, based upon input from the evaporator temperature sensor. The signal from the pushbutton unit goes out to the high/low pressure switch (the one that's not red) on the dryer. From there the signal goes to the compressor control relay AKA the Klima relay. The Klima relay translates the low-power signal from the PBU to a high-power feed which can activate the compressor clutch. The Klima relay also monitors the engine speed and the compressor speed (via the speed sensor on the back of the compressor) and compares the two. If the two are sufficiently different, it cuts out the compressor until the engine is stopped & restarted. This is the most common failure mode on the w124 a/c. About 99% of the time it's a false alarm, but that other 1% it's the difference between driving home & hitchhiking.
Are you certain the signal to the low/high pressure switch is +12v? Have you measured that while the compressor is on? I think that it should be, but on my 1987 300TDT the signal is ground.
Anyways, if you are certain about the absence of +12v it's time to look insode the car. I'd start with the evaporator temperature sensor. It should have a specific temp/impedance curve. I have occasionally heard of them failing, causing intermittent or hard failed a/c operation.