Power antenna will not go down and runs when vehicle is off

Welcome back. That description sounds like the antenna drive has failed inside the motor itself. The antenna uses a spool of basically weed trimmer type plastic to push the antenna up and pull it down. It determines if the antenna is up or down by sensing the current draw on the motor and when it reaches either up or down it trips a latching relay which turns off the motor but sets it to move the opposite direction when power is switched on or off. In your case the broken internal cable doesn't stop the motor turning so the relay isn't triggered. GM used to make a kit to replace the plastic cable and mast part #22109894. Here is a video showing most of the process. To keep it from draining the battery you can remove the fuse that powers it until you can repair it, it is not in the fuse panel but is an inline fuse that will be near the fuse box and is a 10 amp in a red power wire. Most of them will have a strip on them saying either ant or power ant.

https://www.youtube.com/watch?v=FsrPJEWaV7g