Dale
The compressor's primary function is to operate trailer brakes on trailers that are fitted with air brake systems.
Secondary function is to air assist the PTO clutch via switches over the clutch pedal and under the PTO clutch lever. there is a solenoid under the floor on the left side of the cab, on the main airline.
There is an air tapping on the side of the pressure regulator under a removable cover that is prevented from being lost by a plastic strap. Supplied with the tractor was an airline hose with a tyre inflator that screws onto this tapping. This operates directly from the compressor and does not come from the air tank, so will pump pressures higher than that in the air tank.
Air has nothing to do with the diff lock. Suggest you look and lubricate the pedal pivot and linkage, and make sure the rod ends and the pivot are not worn so that the pedal is not pulling the rod far enough. I think this can be adjusted by rotating the clevis on the end of the rod.
Dave