If I'm not mistaken the low pressure switch should be on the accumulator. I did an engine compartment restoration on an 84 Cutlass back in the mid 90's. The car ended up being took apart for about a year. When I got it back together, the A/C didn't work and it had worked fine when I pulled the engine (I left the compressor connected to the hoses to keep the system in tact). I jumped across the low side connector and the compressor ran and the low side immediately got cold. I pulled the jumper wire, plugged the connector back into the switch and the A/C worked fine. The low pressure switch was apparently hung up. Maybe that is your problem.
You may want to put some gauges on that thing before you hot wire the compressor to see if it has any charge. Visual inspection, look at the condition of the hose assembly, particularly the rubber. Look at all the connections for oiliness as an oily connection betrays a leak. Also look at the front of the compressor for an oily mess as that could indicate a leak at the front seal. If everything looks good, it has refrigerant and it won't run, then suspect the low pressure switch. Hotwire it and see what happens.
If you get into the system, I would pull it apart at the orifice tube and look for trash in the screen. It that looks good, go back with a new orifice tube and a new accumulator, pull a vacuum on it and see if it holds. If it does, you should be good to go. Oh, one other thing. If the connections are real oily, the system may need some oil put in it. You can do that without opening the system with a can of oil charge (oil in a pressurized can with a little refrigerant). Is it still R12 or has it been retrofitted to R134A? If it has been retrofitted you might want to upgrade the condenser to a parallel flow unit, which will improve the system performance at low RPM (idling) and low speed. If I forgot anything post more questions. I'm happy to help (or at least try to help).