The rear door trim comes off easily. Just remove the 2 screws and then it is only held on by metal clips that release when you pull. That should give you access to the locking motor. You could disconnect it from the Jeep, then see if it runs by applying 12volt DC to the leads. If it doesn’t, then the motor is the culprit. It could also just be a loose connection since the gate gets opened and shut constantly. I suspect something local to the lift gate since the rest of your locks and electronics work fine.

Not sure if the KK has the same type of latch as the KA, but if it does you can manually lock the gate by rotating a white knob on the latch/lock mechanism. It is behind the gate trim. 1/16th turn counter clockwise will lock it. Turn other way to unlock.
Just remember, if it will not unlock, you will have to climb back there to unlock it.
You can access the knob with the main panel in place. You open the small access panel by pulling on the bottom, then sliding it down.(if it is the same as the KA) The KK manual just says to use a trim stick to remove it.
You can also open the gate from the inside by removing the access panel and pushing the latch release lever down.