Gin's path is an odd one. I stumbled into it on complete accident my first playthrough, but failed to get it when I intended to actually take it on a later playthrough. There's one sequence where you talk to Gin about a meeting with a Shomonkai member when you get a choice between two seemingly innocuous conversation options, and giving the wrong response prevents access to both Gin and Atsuro's paths.
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http://www.nbc.com/parks-and-recreation/exclusives/ron-dancing-animated.gif