Sam, that sure looks like my old saddle!
I had a D ring installed up next to the Cantle on the right side of the saddle as you sit. I tie the rifle scabbord on the right side with the butt up, with the muzzle end of the scabbord tied to the front side of the right stirrup. The rifle swings freely for you to use your spurs and heels on the horse as necessary. I pull the rifle out of the saddle as I am getting off, horse or mule knows to plant their feet as I pull the rifle out of the scabbord.
I can't handle a rifle under my leg...leg goes to sleep.
My mules would usually see the game first, even bedded down. They would stop and stare at the game, time to glass, but you had better pull the rifle out of the scabbord and get off with the same motion.
I have this one horse that would start clearing his nose when he got around pigs or bears. He would plant all 4 feet when he heard them or saw them move, like riding big bird dogs.
