HelloCustomerfrom what you described i would replace the push button or pad for the lift gate. If everything else is working like the key fob and the console button that's what i would replace. If there were a problem with the module or motor then it wouldn't matter which button you pressed the lift gate would not open. I have replaced a few for being non function when button was pressed.
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I'll post the procedure below.Hope this helps.
Remove the liftgate trim panel. Refer to Liftgate Trim Panel Replacement.
Liftgate Close Switch
Disconnect the electrical connector.
Liftgate Trim Panel Replacement (Acadia or OUTLOOK)
Remove the liftgate window garnish molding. Refer to Liftgate Garnish Molding Replacement.
Liftgate Inside Pull Handle Cover
Liftgate Trim Finish Panel Screw (Qty: 2)
Notice: Refer to Fastener Notice in the Preface section.
Tighten2 N·m (18 lb in)
Liftgate Trim Finish Panel Push Pin Retainer (Qty: 2)
Liftgate Trim Finish Panel Retainer (Qty: 6)
Liftgate Trim Finish Panel Assembly
Liftgate Garnish Molding Replacement (E61)
Liftgate Actuator Rod
Liftgate Actuator Rod Stud
Tighten20 N·m (15 lb ft)
Liftgate Upper Trim Finish Panel Assembly
IF THIS HAS HELPED YOU OUT PLEASE HIT THE ACCEPT BUTTON OTHERWISE I DO NOT RECEIVE CREDIT. THANK YOU.