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Do you have a functional key fob that you use to lock and unlock the doors? If you do still have a key fob then the fob itself could be your issue, assuming this happens when you're in range of the vehicle when this happens. It's not uncommon for a key fob to send a signal on it's own, and it's always possible that a button is being inadvertently pressed if the fob is in a pocket. Try removing the battery from the fob(s) and see if this still happens and if not then you know it was a fob issue.
If that doesn't help then the problem could be the liftgate control module or possibly the body control module. The keyless entry signal is picked up and interpreted by the liftgate module which then sends messages out over the communication bus network to other modules. If the liftgate module is reporting key fob signals when there aren't then this will happen, or the BCM could be the issue.
It's also possible for radio frequency interference to cause problems like this. If the problem only happens when the vehicle is parked in a certain place then it could be happening because of something transmitting from another device.
The issue you had with the liftgate really shouldn't be related to what you are having now.
It could still definitely be the liftgate module. The module is mounted directly to the liftgate, it's on the left side and accessed by removing the trim panel.
If you replaced it yourself then you'd save a little bit of money on labor, probably about a half hour worth.
Most independent shops wouldn't have the ability to download the software for a new module.
A used module would obviously already have the software in them but the key fobs would still need to be programmed.