You could write a s script which follows jellyfin logs line for line and greps/seds/awks for a keyword corresponding to starting playback. Then you could extract the file.
It’s also likely that it’s possible to start your specific scheduled task by API like the following [1].
[1] https://github.com/jellyfin/jellyfin/discussions/12224
PS: I don’t know whether it’s possible to run a scheduled task for a specific file only. But I’ve already written the above anyway.
You’d need a second Signal instance. There’s only global privacy options.