Hey KC, I have not set up a systemd timer for my toolbox, but I had some ideas.
The directory for user units should be ~/.config/systemd/user (not systemctl).
But even with the correct directory, systemd doesn’t run inside of toolbox [1]. I’ve run into not having systemd a few times but there’s usually a workaround. Have you considered using your host systemd to run the daemon inside your container? Might be as easy as adding “toolbox run” to the beginning of your ExecStart.