Note that shooting with one lens obscured does not mean that eye is closed, it means that you can't see past the lens.
In any action shooting discipline, you really want both eyes open. It will increase your situational awareness and speed.
When one eye is closed or it covered and receives much less light than the other, the "open" eye will sympathetically dilate the "open" eye. That along with the muscle contraction between sides of your face will reduce the acuity of your open eye. If you must occlude one eye for stationary target shooting, a much better idea is you cover one lens of your shooting glasses with a piece of scotch tape so that the light still enters your eye, but you cannot focus through your off-eye.
When shooting iron sights under compromised target contrast conditions, I find that having more visual information from it coming in through both eyes helps in sight picture definition.