One of Gideon's most defining personal characteristics is his love of birds. He is an avid bird-watcher and has a deep knowledge of all things avian, something that once even assisted him in solving a case. It was Gideon's expertise in mockingbirds that helped the BAU track down unsub Tobias Hankel (James Van Der Beek), one of the killers from the show that fans find sympathetic.
The writers seemingly played on Gideon's connection to birds when it came time to introduce his successor. Viewers first met Rossi in the season 3 episode "About Face." In the opening moments, the camera pans over a pristine wetland in Virginia, complete with a flock of ducks flying overhead. It then cut to Rossi crouched on the banks of the reservoir with a shotgun in hand. He shoots one of the birds, and his dog splashes into the water to go retrieve it.
The show doesn't explicitly tie this scene to Gideon, however, considering the former special agent's affinity for birds, it's hard to imagine that Rossi's duck hunting debut wasn't meant to be thematically related. The image of him shooting a bird out of the sky could be read as the official moment that marked the end of Gideon's run on the series. Although Gideon the character isn't dead (yet), he may as well be as far as the viewer is concerned, as he never makes another on-screen appearance (except in flashbacks).
And to make the moment even more resonant, bird imagery appeared again when Gideon actually did die on the show.