Rear wiper works 3 times and quits motor works with aux power

Sounds like a wiring problem:
1. One of the wires attached to a pin in the connector attached to the wiring at the motor (not on the motor) may be corroded or have come loose, making intermittent contact, or
2. One of the wires in the harness between the motor and the switch is crimped somewhere around the tailgate and is intermittently opening, or
3. A bad motor ground wire connection at the tailgate.

Did you check fuse's & relays ?
Rear Window Wiper Operation
The rear wiper motor is controlled by the SJB. The SJB supplies power to the rear wiper motor from the integrated rear wiper relay. The SJB will activate the relay when all of the following conditions are met:

• Ignition switch is in the ON position
• Liftgate glass and liftgate are closed
• Multi-function switch is in the ON or intermittent position

The SJB also supplies voltage to the rear wiper motor from SJB fuse 21 (15A) when the ignition switch is in the ON position. This power feed is used to continue the wipe cycle when the multi-function switch is turned to the OFF position. The SJB receives inputs from the multi-function switch that applies ground to the low speed wipe input or applies ground to the intermittent wipe input. When either of these circuits are grounded, the SJB activates the integrated rear wiper relay and power is supplied to the rear wiper motor to move the rear wiper motor from the park position. An internal switch in the rear wiper motor then moves to the run position which connects the accessory relay power to the rear wiper motor. When the rear wiper motor returns to the park position, the internal switch in the rear wiper motor moves back to the park position. If the multi-function switch is in the ON position, the rear wiper relay is still activated, power is supplied to the rear wiper motor, and the wipe cycle starts again. If the multi-function switch is in the intermittent position, the rear wiper relay does not activate until the predetermined dwell time has elapsed, at which time the SJB activates the rear wiper relay and the wipe cycle starts again. The SJB is the smart junction box .(computer )

Rear Washer System
The SJB supplies power to the rear washer pump from fuse 21 (15A) when the ignition switch is in the ON or ACC position. The rear washer pump receives ground from the multi-function switch when the wash function is turned ON. The multi-function switch also signals the SJB when the rear wash is activated and the SJB then activates the rear wiper.

Do you know how these wipers Work / what controls them ? Do you know what a smart junction box is ?
Rear Window Wiper Operation
The rear wiper motor is controlled by the SJB. The SJB supplies power to the rear wiper motor from the integrated rear wiper relay. The SJB will activate the relay when all of the following conditions are met:

• Ignition switch is in the ON position
• Liftgate glass and liftgate are closed
• Multifunction switch is in the ON or INTERMITTENT position

The SJB also supplies voltage to the rear wiper motor from SJB fuse 21 (10A) when the ignition switch is in the ON position. This power feed is used to continue the wipe cycle when the multifunction switch is turned to the OFF position. The SJB receives inputs from the multifunction switch that applies ground to the low speed wipe input or applies ground to the intermittent wipe input. When either of these circuits are grounded, the SJB activates the integrated rear wiper relay and power is supplied to the rear wiper motor to move the rear wiper motor from the PARK position. An internal switch in the rear wiper motor then moves to the RUN position which connects the accessory relay power to the rear wiper motor. When the rear wiper motor returns to the PARK position, the internal switch in the rear wiper motor moves back to the PARK position. If the multifunction switch is in the ON position, the rear wiper relay is still activated, power is supplied to the rear wiper motor, and the wipe cycle starts again. If the multifunction switch is in the INTERMITTENT position, the rear wiper relay does not activate until the predetermined dwell time has elapsed, at which time the SJB activates the rear wiper relay and the wipe cycle starts again.

Do you know what DTC'S - diagnostic trouble codes are ?
Smart Junction Box (SJB) Diagnostic Trouble Code (DTC) Index DTC Description Source Action B1244 Wiper Rear Motor Run Relay Coil Circuit Failure SJB If the rear wiper is inoperative, Go To Pinpoint Test B . If the rear wiper is always ON, Go To Pinpoint Test D . B1245 Wiper Rear Motor Run Relay Coil Circuit Short to Battery SJB Go To Pinpoint Test B . B1614 Wiper Rear Mode Select Switch Circuit Failure SJB Go To Pinpoint Test D .
Did you have it checked for DTC'S ?

You might want to check this video.

theres a short sumwhere in wiring

bad ground on motor or bad motor do u know how to test for power going to the wiper?

check main power panel under the hood for aux fuse, should be in the 40 to 60 amp range possibly slightly larger than standard fuses.

1. check the fuse to the rear wiper motor
2. check for power to rear wiper motor at the motor (power wire going in to the wiper motor with rear wiper switch on)
If you have good fuses & have power going in to the rear wiper motor...
3. Pull old rear wiper motor and install a new rear wiper motor.
Thank you please drive thru......

It is the Motor. This is a VERY Common GM Problem that they have not Fixed since 1990. You will need to remove the Rear Door Panel to Access the Motor.

check for power at the wiper motor. If power at the wiper motor but no wiper action then replace the motor. if no power at the motor then use a jumper wire and put power to the motor. Does motor run? if so check for open circuit in the wire someplace.