Automatic tailgate goes up and down by itself?

It could be a loose ground, corroded electrical connector at the BCM or tailgate control module or either of these can be bad. We should do a CAN scan to see if there are any codes which can help us fix it. You can get a CAN scanner (Controller Area Network) which will work on most cars from Amazon.

Here is a video to show you how:

https://youtu.be/u-4syLc-ifQ

Here are the locations of the BCM and tailgate control module so you can check the electrical connectors. I also included the tailgate wiring diagrams so you can see how the system works.

Power Liftgate Initialization
General Procedure

NOTE: The power liftgate may not operate correctly under the following conditions:

A low voltage or dead battery
A disconnected battery
Repairs/adjustments have been made to the power liftgate rod, power liftgate motor, liftgate hinges or liftgate striker
If any of these conditions has occurred, the power liftgate must be reinitialized.
NOTE: Battery power must be removed from the LTM for 20 seconds before the LTM will enter the initialization mode.

Disconnect the battery or remove the LTM fuse(s).
Wait 20 seconds and reconnect the battery or reinstall the LTM fuse(s).
If liftgate is not already in the fully closed position, manually close and fully latch the power liftgate.
NOTE: Make sure the power liftgate system is turned ON in the message center before performing this step.

NOTE: If the power liftgate does not open during this step, Refer to Power Liftgate to diagnose the inoperative power liftgate.

Power open the power liftgate by using the RKE transmitter or instrument panel control switch.
Once the power liftgate is fully open, close the power liftgate by using the RKE transmitter or instrument panel control switch.

Check out the images (below). Please upload pictures or videos in your response of any problems so we can see what to help you with.