I am not a doctor, nor do I play one on TV, but I would like to ask you one question.
Are you easily startled by loud noises or bright flashes? I ask because if so it may be hard to beat the blink. The blink is an involuntary reflex from your brain to protect your vision.
I did it when I was young, I have worked for a long time to beat it and finally managed to do it, how, you ask.
It is a mindset, you have to train your mind to accept the fact that every loud noise you hear is not out to get you (I know, sounds dumb) But I am at the point of being able to keep both eyes open no matter what I hear or see, And have been there for years, (I am 56 years old) I have been a mechanic for almost 40 years, so I have an almost never ending supply of loud noise to practice with.
You probably have been blinking all of your life, but with declining eyesight it becomes more noticeable due to the extra time it takes to refocus after the blink.
Here are a couple of tricks to possibly help retrain your brain, Have a friend or relative come up behind you and clap thier hands or slam a book on the table, maybe trigger a camera flash from behind you, keep this up at irregular intervals when you are NOT expecting it, also when you are shooting, apply the follow thru suggestion that was mentioned earlier, WATCH the bullet go into the target (the same way you would watch a bowling ball strike the pins) don't assume it will hit the bull, MAKE it hit the bull, guide it with your eyes, ( I know it really won't work, but it will help you keep your eyes open).
Long winded I know, but fi it helps I guess it was worth it.
Good luck in your battle