Both eyes open even with iron sights, unless you have some vision abnormality.
Fer instance. About a year ago I had Lasik mono vision, near right (dominant) eye, far left eye. I can focus on the front site again! yeah. Problem is now I see the front sight clearly and the target clearly but its got bad parallax -- after almost a year I'm finally getting my brain "retrained" to get a consistent sight picture, but i have to close by left eye for precise shots like a 3" triangle steel plate at 15 yards, the 5" square and 8" circle I miss only if I'm trying to improve my speed, but the 3" triangle its close one eye or be really slow.