When threatened, under stress, or when fight or flight kicks in, that adrenaline dump will not let you naturally close one eye. Won’t happen. So why don’t ppl train with the body’s natural action/reaction?
Hopefully you are right/left eye dominant and a right/left handed shooter, which makes this task a helluva a lot easier.
We were taught to take up your natural shooting stance, aim in, and then “squint” (not close) your non-dominant eye. It felt awkward at first, but after thousands of both dry fire and live fire reps, it became a non-issue.
As always, when you practice shooting with both eyes open, focus on the front sight vice the target. No different that looking down to the tip of your nose. The dominant eye will automatically take over, while the non-dominant eye won’t even attempt to input info to the brain. If that’s difficult to do, apply some scotch tape to the non-dominant safety glass lense. It’s will be hazy/fuzzy, but allows both eyes to remain open. When you bring the gun up, you should still be able to see your front/rear sights and line them up properly. Hope these tips help! Stay safe.