the early E34s (& E36s) had multiple issues w/ceramic resistors for the aux fan. I felt the same as you, I didn't trust the temp sensors so I put in a toggle switch where I can manually turn on aux fan if temp ever did/does climb. I connected the wires to the relay (brown relay) in the relay control box (3x5" box driv side -top of wheel well) one side to blue wire, other side to green wire. I only use it when in heavy traffic and using A/C - just added insurance against overheating.
Another note - E34 engine compartments handle ALOT of heat so the more air flow the better. I had the hood louvered and that dropped temp by some 20-30 degrees, but you need not go that extreme. On the pass side just behind headlamps is a black plastic circular plug about 5"s across, pop that out and you'll notice that she'll run cooler also. (that plug is same size as air filter intake on drivers' side)
To answer your initial problem - try the above mentioned switch on relay, make sure ALL your fuses are good and evac & refill your A/C (4lbs MAX) - prior to charging system add AC oil & AC sealant (since you mentioned prior owner let it sit for long time) I'm betting you'll have cold AC without having to buy a compressor.