I believe the module is in the trunk behind the LH tail light, near the fuel cutoff switch.
7 hours is way too long, but it sounds like they're not charging you for that whole time. If they want to charge any more than that; I would complain to the manager. The dealer works on these cars every day, so they should be able to diagnose it pretty quick. Any more money than the $300 and you could have bought a tuner or chip and turned PATS off that way.