I like using both eyes for several reasons.

It keeps you more aware of movement including the deer, and other things around him. Also, I find that I shoot best (bows, guns, whatever) when I can relax my face and get completely in the zone. I let my face go blank and then focussing on the task of shooting becomes easier. Trying to hold a squintto keep one eye closed is a distraction and you will fatigue quickly, and start to tremble.