Good question! I stillhunt with both gun and bow, and what I've used for many years now for the gun is an elastic sling. It's not meant to be slung over a single shoulder (although you can do that with it), but draped around the shoulder and across the back as shown in the picture.
It can be carried pushed out of the way and on your back...muzzle pointing towards the ground...or you can carry it slung across your front and low to one side. It's VERY easy to bring it up to mount, and the elastic will pull the stock in towards you for a firmer anchor.
I also wear a bino-harness, and I put that on first and then the gun/sling goes over it. Then you can simply slide it out of the way when you want to glass.
Another thing about this set up that I like a lot for stillhunting is that it's very quiet, there's a minimal amount of movemnet that you must engage in to use it, and because the trigger/bolt/magazine area is right there at you side at arm's length, you can easily check you safety....which is something I do very frequently and without thinking about it. When you hunt in heavier cover and are kneeling/squatting/sitting a lot that's a REAL good idea.
I was turned on to this by my good friend and hunting buddy who is a Vietnam vet and the weapon he carried in Nam had a similar type set up.
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NRA Endowment Life Member