There is a problem of some kind with the wiring harness connection, the ground lead has been faulty for some. Heard today the AC Delco replacement pump comes with a replacement plug. Had another tow truck driver tell me he jumpered the ground lead across that after market harness plug and made his sporadic running issue go away. However, I did not hear him say his pump continued to run after the ignition was off, I do not think mine has done that. Are you sure it isn't your AC lines equalizing out after the shutdown?
From what I heard today from a GM Master mechanic and my issues related in the link below we are crazy if we use other than AC Delco replacement pumps.
I have a 97 GMC Yukon (same as a 97 Tahoe) the pressure regulator valve leaked. On a 97 the upper plenum opening and closing job to get to that $90 valve is about $700 labor and new seals. Half the upper engine hardware is mounted off that plenum. I got about 210K before mine was detected as leaking, but not seriously. However it has to be a potential fire fuel producer, so it needs to get fixed if you have a leaker.
Related issue from me.