An enlisted airman couldn’t keep a gun in his possession at the bases I was at from 1963 to 1967. Any Personal weapons were kept at the Armory and had to be checked out if the owner wanted to use them.
I think that was for those who lived in the barracks. Maybe even in military housing. I know I, and two others, took shotguns onto a base without having to even register them with the APs or other other base officials. I think we did mention to the gate guards, which could have been military or police, that we had them in the vehicle.