1992 Buick Park Avenue air ride

This could be a variety of things. You may have a bend strut or bad strut on that side. Your pump can be diagnosed by unplugging both tubes from the struts themselves. Let the air out - turn the car on - If the pump doesn't come on then you have a problem in that area. if the pump works you should feel air coming our of both sides. If only one side has air then trace back and see if you can find a kink in the line. This is rare though. If everything checks out - air coming out of both sides - then you probably need new struts.
Side note - there should be a height sensor near the rear end. If this is in the wrong position, your pump will not kick on. When you do your test, and nothing happens make sure that the sensor is not stuck or in a position that reads the rear end is at a good height. Simply moving the sensor all the way in either direction should kick the pump on. This is normally not an immediate kick on. it may take a couple minutes
I hope this helps
Sarge M179708