Yep, atu might be correct there, about eye dominance. (you can train yourself to use the other eye, but it's not as easy to just do. For some, anyway. ) With digital cameras, shooting left-eyed is usually no biggie. It was a bigger deal back when there was an advance lever to poke the left-eyed shooter.
When using one eye or the other, while keeping both eyes open, it's more like shifting your attention between these eyes (like you might do if you simply hold a hand in front of one eye or the other)
The idea here is you want both eyes to be pretty relaxed, whichever you use. It becomes quite natural.