I'm of the belief that if we were designed to do ANYTHING with one eye closed we would only have one to start with.

Generally a person who shoots a bit better with one eye closed on the range has an eye dominance issue. (left eye dominant shooting Rh or vice versa)

That person would be better served just slightly squinting down on that dominant eye vs closing it entirely.

When you shut one eye you mess up your depth perception, light gathering and balance which isn't the greatest combination of things to be taking away 20ft up in a treestand.

Shooting with one eye completely shut is maybethe LAST thing I would recommend any shooter do unless they are sitting behind a scoped rifle.