How do I make tag sets searchable in Find Contacts?
Matthew, welcome to the CiviCRM community.

Have a look at http://book.civicrm.org/user/organising-your-data/groups-and-tags/ - there's a section on using Tag Sets.

It does say "adding them creates an additional search field in the Basic Criteria section of the Advanced Search" indicating that they are not available in the Find Contacts search.