Shooting with both eyes open is the best idea
if you can do it. Not everyone can because of the physiology of vision. I'm lucky and shoot everything with both eyes open, including scoped rifles (expect when using higher magnification scopes).
Determining eye dominance is always an important first step. See
here or
here.
If one is cross dominant, i. e., the dominant eye is on the side different from the dominant hand, one can often learn to shoot a handgun with both eyes open. The trick is developing the habit of turning the head slightly to line up the dominant eye with the sights. Managing long guns is another matter and closing one eye will usually be necessary.
Some people are have a weakly dominant eye. Sometimes when fatigued the non-dominant eye will try to take over. These sorts of factors can complicate or even prevent learning to shoot with both eyes open.