The problem your talking about is called shortcycling,
the shortage of gas, the compressor will run until it
reaches normal operating pressures, when will continue
to drop till it cutouts.
Yes our cars have HIGH AND LOW pressure cutouts, and a
pressure relief valve, these are standard items found
on an air conditioning system.
You can jump the safety switch, at the bottom of the
right fender well, there is a 4-wire switch pressure
switch there, connected to a small silver cylindrical
tank. I am not sure of which of the 2 wires it is