Too bad that the GPU manager process isn't obvious in your situation. If you are comfortable with command line tools you might want to run a little batch script to monitor GPU usage. I'm guessing Windows still has Task Scheduler? If not, something like ZCron should do the trick. With either of those and a small batch script, it should be fairly straight forward to check GPU usage every five minutes or so, then initiate a shutdown based on the results. If you do go down that rout, I suggest only shutting down after two or three successive GPU checks that are all below your threshold, to avoid accidentally shutting down if the GPU check just happens to be in-between frames. I learned that the hard way.
Another option is using one of the free render management tools out there. Most of them can be configured to run a particular script on job completion. Honestly, though, getting them properly configured is probably more of a hassle than writing a cron job or a batch file script.
I realize this is not the kind of answer you were looking for. I haven't been a regular Windows user in many years, so there is probably a more GUI driven solution out there. In real life, if you're not already familiar with cron job or .bat files, it will probably take a full day to get a cron or batch approach working reliably.
Good luck!
(edit)
A little googling has turned up this utility:
https://processhacker.sourceforge.io/Looks like it can track GPU usage and has triggerable events. It might do exactly what you are looking for.