I'm not a competitor but continually improving my shooting skills is what drives me.
Along the lines of blinking, I spend and have spent a lot of time behind glass for long periods which causes facial fatigue. I trained myself to use single eye optics with both eyes open. it just takes reps and the decision to be intentional.
Same with blinking. I used long range 22LR semi-auto in part to train out blinking. Seeing the bullet in flight and the hit in the scope is pretty cool. Training on a small rifle obviously scales up to larger cartridges. Seeing bullet trace and the hit in the scope never gets old.
Bandwidth might be a better way to say this. During the entire shot process until it starts over, I'm so focused on the shot process and input from the scope, my brain doesn't have the bandwidth to blink because it's tasked with getting information. Getting visual information is prioritized over blinking.
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You can't see my other eye, but I'm shooting a 100yd 10 shot/60 second drill with both eyes open. The goal is 1.5" or less for 10 in under 60 seconds, not just shooting fast.
My body knows how to run the bolt so my brain is watching through the scope and correcting sight alignment the entire time. As soon as the bolt is closed, final sight refinement begins as I begin to press the trigger within wobble limits.
The shot is not "timed", the shot process is compressed to do it quickly but correctly.
Most people I've been around are pretty casual about shooting, thus they learn/improve slower.
A course like S2H or just friendly challenges can be beneficial because humans naturally want to be as good or better than the other guy. When the guy next to you is shooting smaller groups and/or doing it faster, you try harder to get better.
Being intentional with every shot is learning with every shot.