You need to get the full schematic and trace through the whole circuit. It appears that one of the temperature switches is designed to open if the engine starts to overheat, which shuts down the compressor. So this switch should be closed circuit normally (not overheated). It is in series with the pressure switch. Both must be closed for the compressor to come on.
The 4-wire pressure switch probably has one circuit for the compressor and another for the fans. This means that if you unplug the switch to jump it, the fans will not respond to refrigerant pressure. Running the compressor with no fans will cause an overpressure which-- without the pressure switch operational-- will blow a hose or pop the relief valve. So if you go jumping things and the compressor does start, do it for only a very short time (a second or two) so that pressure does not build up.