Is there a gnome Phase 2?
No. There's no Phase 2. It's just another fetch quest to add another Facebook friend (counts towards perks), earn some XP and money, and half of an achievement (along with befriending the Crab People).
The name 'Phase One' is a joke which calls back to the original Underpants Gnome appearance on South Park:
The lack of a second phase is kind of the joke.