I have shot handgun for a long time since age ten, and have always used the one eye approach for target work.
Since I am right handed and left eye dominant, using both eyes open just creates a confused situation for my body to deal with. Once upon a time up until around age 40 I could shoot almost equally as well using my left hand, but even then a one eye approach was the only one that worked for proper sight picture.
I either close my left eye or use a piece of cardboard (cardboard from a 22lr brick works well) cut and bent to shape with tape to hold in place to cover the left lens of the shooting glasses. I do not like sticky residue on the lens from direct tape.
From reading, I would say that in combat situations with a handgun it is always best to use a two eyes open approach for a number of reasons with the most important being full peripheral vision in order to be aware of surroundings.
For rifle with iron sights I also close the left eye to reduce confusion with my brain processing info.
For trap/skeet I need to keep both eyes open. This is especially true for skeet where you need to have full peripheral in order to pick up the clays from the sides in order to get on target quickly. My father was the one who got me started on clays, and he told me it was only going to work with both eyes open. He coached me in the beginning as I had a lot of issues trying to scan the periphery to get on a swinging arc with the target and then have the correct sight picture when pulling the trigger. It took a LOT of practice to get there for me. It takes someone standing behind you to figure out where you are actually shooting and to discuss what you are seeing with so you can make adjustments. I had to overcome the whole dominant eye - opposing dominant hand thing. Once you imprint in your brain what a sight picture should look like for swing and lead, and then what it should look like when you pull the trigger, it will become natural regardless of what your brain would interpret otherwise.