Once the 12V on the trailer harness turns on, it'll stay on even if it's placed back into park. You don't actually have to move the vehicle to turn on the 12V, just shifting to reverse or drive for 2-3 seconds is good enough.
Your problem might actually be that the battery in your trailer is...
I don't have a Gen14 yet, but on my 2015, the trailer 7-pin cable only energizes the 12V pin after a trailer has been detected and is put into drive or reverse for three seconds. It will stay energized even if you put it in back into park but will turn off as soon as the trailer cable is...