Are you SURE it's the compressor kicking on/off?

The late model trucks, Troopers and Rodeos that have the 4L30
transmission will do a systems check when sitting idle, in gear.
When the trans does the system check, it will cause the truck
to lurch forward very slightly and yes, it feels just like
the compressor kicking off.

If you stop at a light for 15-20 seconds, you'll feel the lurch.

If it is the compressor kicking on and off, you should feel
it multiple times while sitting idle, in gear.

1995 Trooper LS auto 3.2 DOHC /w SOHC intake
1989 Trooper 2.6 auto
1989 I-Mark RS DOHC 1.6
1991 Stylus XS DOHC 1.8