Sometimes both eyes closed
At least it seems that way after looking at the target.
being serious now. Both eyes open because that is how I was taught too long ago. I shoot right hand with a right hand rifle but I'm left eye dominant. Even when shooting pistols, I look thru the sights with my left eye.
This gets harder as I get older. I have tried to work from the other side and I have equal success that way but for me it just isn't right.