Try jumpering that switch anyway, as it may be bad. It's a combo low/high pressure cutoff IIRC.

I'd download the 89 factory service manual and start wading thru the wiring diagram. It's hairy, really complicated. I can't remember for sure, but there may be a high coolant temp switch in the circuit, too, somewhere on the t'stat housing. There's a heater relay and an a/c relay in the circuit, too, and iirc, more than one fuse. I'd start at the a/c switch with a voltmeter or test light and start looking for where the power stops.

Or just wire in a new compressor switch from ign on to the a/c compressor, but you lose all the safeties that way...