You can already do this.
The only reason it doesn't come up automatically is because you don't yet have all the rep-based privileges. I'll show you how to do this based on screenshots from my account on a site where I don't have all the privileges.
First, go to the box in the top left of your Activity page and click the little wheel to change from tracking a privilege to tracking a tag badge:
Once you've set it to track a tag badge instead of a privilege, you can then choose which tag badge to track by clicking the other little wheel on the left:
You'll then get a popup window with all the possible tag badges you can track. Have fun!