what is the pump? in the rear of my buick park avenue for?runs off and on

The only two pumps that I know of that would be in the back of a car would be either the fuel pump - "generally in the gas tank". Or an air compressor - maybe the car has an auto ride feature and it is a compressor for the shocks. Not sure if that helps. But would most likely be one of those..

A 2002 Buick Park Ave, does not have air-ride suspension. Mac-Strut front and Semi-trailing arm rear suspension (http://www.edmunds.com/buick/park-avenue/2002/sedan/features-specs/) so no compressor. You are hearing the fuel pump. All is well

In tank fuel pump going bad. Normally, does make some noise. Turn key to on but don't crank. You will hear pump cycle. If it has vibrating noise, it's going bad. You have to drop fuel tank to service. This is best left for dealership. Straps holding tank usually rusted. Your car does have an air compressor for ride level. There is air ride from factory, unless someone replaced oem struts and shocks with non oem type. I am not sure of compressor location. Look up at GM parts dealer. Compressor still available, but very costly. Same part 2000-2005

From about 99 to 04 and maybe more years you don't need to drop tank to change fuel pump. There is an access plate to get to it from the inside the trunk