Trying to close one eye while aiming does use more facial muscles than keeping both eyes open.
In a weekend long competition, using those extra muscles does tire you out quicker.
Try walking around and keep one eye closed.
"A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed."
Life Member NRA
Life Member NAHC
Former President of the ECPT (Eifel Combat Pistol Team)