I had a 1990 C1500 and currently have a 1995 C1500 and both of them have this problem. On my 1995 (183,000 miles) I replaced all of the tie rod ends, pitman arm, and idler arm and it still does it also. I am starting to wonder if I have a bad bushing or if has something to do with an aging frame or springs. Mine seems sort of like axle wrap/wheel hop, I'm going to have my drums turned and put on new rear brakes to see if it helps.
If you need scrap yours, I'll come hall it off for ya' /forums/images/graemlins/thumb.gif /forums/images/graemlins/rotfl.gif