Pretty much every Fort or Base had their own Rod and Gun Club - and they all had patches.
At least, they did until it became no longer popular, and they started closing the golf courses and amalgamating the various Clubs and minimizing the shooting sports, entirely.
At one time, you could always find the Old Man and the Top or the CSM out at the Trap Range on a weekend - just like you saw John Wayne doing in 'The Green Berets'.
Today, those activities are suspect - and this from Combat Arms guys...
It was a great time to serve, though - no political correctness, no 'real' chickenshit - everybody had a focus, and knew what they were about.
Today - not so much, as too many became 'self-polishing apples' and would game the system in order to advance.
But I digress...
The old Rod and Gun Clubs were where you could order all manner of guns and fishing 'stuff' and get a bargain in the process, they were a perk of military service that civilians didn't enjoy, and a lot of 'business' and mentoring could be discussed at the Club or Range or on the links that wasn't 'official' - and there was great value in that.