Has Anybody Consulted The GM Technical Service Bulletin Pertaining To The ABS Light And A Revised ABS Wheel Speed Sensor Jumper Wiring Harness ? It Includes The 2001 - 2004 Grand Prix Models.
The harness part numbers (R & L available) are listed and instructions for splicing.
Don’t know if this will fix your problem, but you do need a technician that can access and use the bulletin and properly diagnose and resolve this problem.
CSA