Fools Sulphur (love the name!), what you speak of is known elsewhere in the shooting sports as the Natural Point Of Aim, or NPA. It's where the relaxed muscular-skeletal system points the rifle with no steering. NPA is important in all shooting positions, but critical in offhand, aka standing because the shooter's only contact with Mother Earth is two small feet a long way from the rifle.
It takes a while to learn the feel of a good NPA. I find dry firing to be some of the best raining I do. With a double set trigger and the hammer/cock full forward dry firing will show you if NPA is right. Did the front sight drift off to the left as you "fired" and followed through? If yes, your NPA was off, and it's time for a tiny shift to the right. NPA also has a vertical component.
So, let's all get cockin' and clickin' to get ready for better weather!
White Fox