"People who" is your indicator here. Group 1. "Not" is only functioning as a negation of handsome. There may be some exception I'm not aware of, but I don't think "not" by itself can function as an indicator. Just a negation.
... only" works as sufficient condition indicator because of its typical placement ... only" is a sufficient condition indicator for "become rich"). But the ... , yet mechanistically applying the sufficient indicator rule could lead you to ...