@silmathoron It may take * or 0 to mean the same thing in this instance but as you probably know * is a wildcard for any string of characters with any length and /${period} is restricting this to only match if the wildcard number is divisible by the number given.
I use this webpage as a reference:
https://silentlad.com/systemd-timers-oncalendar-(cron)-format-explained
The OnUnitActiveSec takes a seconds value so $((${period} * 60)) should help there. And you can specify if the service uses the WakeSystem.
https://www.man7.org/linux/man-pages/man5/systemd.timer.5.html