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Try to draw when he isn't looking in your direction.
Deerhave a lot of rods in their eyes that are GREAT for picking up contrast and movement.

Draw when his head goes behind a tree or anything that momentarily will obscure his vision. Learning to time itcan take a bit of practice.

Also, in my experience, if you must draw when you can see his eyes, do it when his head is down. If he picks up the movement, he'll bring his head up to look straight at you. You'll buy yourself an extra second to shoot while he repositions himself to get a good look at you.