Derived from Okinawan Mythology, Shishi ward off evil spirits (the one with the open mouth) and keep in good spirits (the one with the closed mouth) and are often found on rooftops or on either side of gates, or as decorative figures. They could be seen throughout Okinawa in my childhood, and I imagine that's still true today. This pair came from an Okinawan store in San Francisco.
(Back in Internetland! Apologies for being behind while traveling again . . . )