Yeah, so the government can track you, and really anyone who gains access to the signature and trust chain can track you. The trust anchor also has to verify your identity to verify your age in order to issue the PEM file.

So to answer my original question - no, you can't anonymously verify age. Someone has to verify your identity (a central authority in my comment, which in your system is a trust anchor) and your signature can be tracked back to you (as a fearure).