I could go on and on about eyes and vision, but that would be boring to most.
Some of the statements above address the idea of a weak and a strong eye. There are many details and ins and outs. I will just make a few comments.
First there is always a dominant eye. If our brains didn't make this so. we would see multiple images and probably get a headache. For a younger person with good vision there is a seamless transition between 1 eye to the other. Enough said about that.
A child or an injured or ill adult may develop a weak eye. There are exercises for this may help this along with patching the eye with an adhesive patch of a "pirate" patch. Sometimes glasses are used and strange as it may seem the purpose of the glass over the good eye of a child is to put a strain on that eye to make it less likely that the brain will favor that eye to the exclusion of the weaker eye. On occasion an operation is needed to get better results.
There is no "real" depth vision with only one eye. Only the illusion the brain and training can bring about. This can be proven with tests that take away any background. i.e. 2 lit signs in total darkness where one is further, but its size and its light has been increased to appear the same. Two good eyes will spot the difference immediately. One eye, never.
When we get very tired, then usually the dominant eye will continue with the load but the weaker eye might take the opportunity to slack off.
I have read for a long time and then varied the tempo by shielding one eye for a period and then the other. It refreshes and rests the shielded eye. Good trick to know.
Some of the problems are accentuated if night vision goggles are used. It has been problem in the past and aircraft have crashed because of it. (And those are binocular goggles.)
A good shooter is trained to keep both eyes open even though they are mainly using only one eye. Some people have a problem with this at first. You will sometimes note that a man has a more pronouncedly open shooting eye. Sorta of a habit. I am that way.
You can learn to cope with an injured dominant eye, just like the amblyopic child learns to cope with a patched dominant eye.
Just try learning to shave or brush your teeth with your "other hand."
Be particularly careful with a straight razor, or rather don't use a straight razor is better advice.