Check this bulletin out and let me know if it helps ok.
#02-08-43-001A: Rear Wiper Jumps When Fog Lamps Turned On (Connect Auxiliary Ground to Rear Washer Pump) - (Mar 24, 2004)
This bulletin is being revised to add models, model years and revise the Parts Information. Please discard Corporate Bulletin Number 02-08-43-001 (Section 08 - Body and Accessories).
Some customers may comment that the rear wiper jumps when the fog lamps are turned on.
Electrical feedback from the fog lamp circuit into the ground of the rear window washer pump may cause this condition.
To perform this correction, you will need to obtain the following items:
Important: Do not re-use the old cable seals. Replace old cable seals with P/N 12041351.
Isolate the rear washer pump ground circuit by performing the following steps.
Tighten Tighten the engine wiring harness ground/negative cable bolt to 25 N·m (18 lb ft).
Tighten Tighten the bolt to 9 N·m (80 lb in).
Tighten Tighten the battery tray bolts to 9 N·m (80 lb in).
Tighten Tighten the battery hold-down retainer bolt to 25 N·m (18 lb ft).
Tighten Tighten the battery cable bolts to 17 N·m (13 lb ft).
Tighten Tighten the front end diagonal brace bolts to 9 N·m (80 lb in).
Parts are currently available from GMSPO.
Have you checked the connections and pass throughs at the rear hatch area? It's possible that ground is open somewhere and the wire is either frayed or open completely.
Schematic Reference: Wiper/Washer Schematics
Connector End View Reference: Wiper/Washer Connector End Views
DEFINITION: The rear wiper motor is inoperative in one or more modes, the rear washer pump may or may not operate.
Did you review the Rear Wiper/Washer System Description and Operation and perform the necessary inspections?
Go to Step 2
Go to Symptoms - Wiper/Washer Systems
Does the rear wiper/washer system operate normally?
Go to Testing for Intermittent Conditions and Poor Connections
Go to Step 3
Did the rear wipers operate in any of the rear wiper/washer switch position?
Go to Step 12
Go to Step 4
Does the rear washer pump operate when the rear washer switch is pressed?
Go to Step 5
Go to Step 10
Did the parameter displayed Open and the Closed accordingly?
Go to Step 6
Go to Courtesy Lamps Always On
Does the test lamp illuminate?
Go to Step 7
Go to Step 9
Connect a test lamp from the battery voltage circuit terminal to the ground circuit terminal in the wiper motor harness connector.
Go to Step 20
Go to Step 8
Repair the rear wiper motor ground circuit for an open or high resistance. Refer to Circuit Testing and to Wiring Repairs .
Is the repair complete?
Go to Step 22
Repair the battery voltage supply circuit for an open or short to ground. Refer to Circuit Testing and to Wiring Repairs .
Go to Step 18
Go to Step 11
Repair the accessory voltage circuit for an open or short to ground. Refer to Circuit Testing and to Wiring Repairs .
Does the rear wipers operate when the rear washer switch is pressed?
Go to Step 13
Go to Step 16
Is the battery voltage present for both rear wiper switch positions?
Go to Step 14
Did the test lamp illuminate in any of the rear wiper switch position?
Go to Step 15
Did you find and correct the condition?
Go to Step 17
Inspect for poor connections at the rear wiper/washer switch. Refer to Testing for Intermittent Conditions and Poor Connections and to Connector Repairs .
Go to Step 19
Replace the rear wiper/washer switch. Refer to Rear Window Wiper and Washer Switch Replacement .
Inspect for poor connections at the rear wiper motor. Refer to Testing for Intermittent Conditions and Poor Connections and to Connector Repairs .
Go to Step 21
Replace the rear wiper motor. Refer to Rear Window Wiper Motor Replacement .
Operate the system in order to verify the repair.
Did you correct the condition?
Go to Step 1