Black wire is ground.
Red wire is +12V supply.
Pink wire is a sense or feedback signal to the 4WD controller.
With the pump air lines disconnected, the pump should run when power is connected between the red & black wires, and stop when the outlet is capped (for example with your finger) - if your pumps do this, they are probably (99% certain) in working order.
Very briefly, here is how it works - a switch on the transfer case is used to tell the 4WD controller, which may be part of the PCM (Powertrain Control Module) or may be stand alone, that 4WD has been selected, at which time the controller will supply +12V to the pump and then monitor the pink wire to determine when the freewheel mechanism has engaged, after which it turns on the 4WD light - if the controller does not see feedback within 10 seconds it will shut off power to the pump.