I'm firearm dependant.
With rifles I'm right hand dominated and I use my right eye through the iron sights and my left eye to view the area. Like many, if I have to time and can see a shot, I'll take my time and pin point it with just my right eye.
With pistols/small-arms, I'm still right hand dominated, but I aim with my left eye down the sights and keep my right eye open to maintain my field of vision.
Out of Sport. Have Fun!