Cold Trigger - My uncle was a famous range master - most police say he was the best ever, though he immediately bought up Gunnery Seargeant Carlos Norman Hathcock III's name if the issue was ever brought up. He said Gunny Hathcock could teach windage better than anyone he ever knew, so at least figure my uncle was pretty doggone good at teaching shooting.
I very clearly recall him scolding me on that very question.
He said, "Now I'm going to tell you, look at the target, but you're a **** college student and you're going to try to line up the target, the front sight, the back sight, and you're going to be shooting all over the place.
If I tell a brick layer, 'Look at the target', he's going to look at the target and he'll out-shoot you for as long a time it takes for you to learn to look at the stinking target."
Now, scopes in a hunt are a bit different. If he's standing, I let my eye peek at a point of aim above the animal, click and hold over for wind, but look at the shoulder blade (or appropriate place on the animal as I break on the trigger. I usually know right about where in the crosshair window I'm using as point of aim, though I don't trust many scopes right down at the bottom of the window. Spherical abberation throws you off a bit on most scopes. Zoom out, and sight him in the good part of the glass.
Practice this on deer and coyote silhouettes until you KNOW your scope's zoom, and how it affects holdover and drop. If he's moving toward cover, don't waste time peeking. Lead him and pull the trigger.
I hope this helps. Humbly, gunsmith.