One thing I was taught in the Army was “point and shoot”, or fire from the hip. I still believe in this. It’s a way to quickly react to something caught in peripheral vision, or a sound from the side or behind, where one can quickly swing on target and let one rip.
I recall being taught the hand/eye coordination using BB guns. It’s amazing how accurate firing from the hip can be at close range.
Also firing pistols left handed is a must. To me it is just totally stupid to expose ones full body and head to shoot around a left corner when exposing only the left side of the head and left arm works.
When I took my concealed weapons test, it included being able to hit a man size target at 25 feet. I used the point and shoot method and hit 100% with my 9mm Norinco Tokarev. The guy up next used that two handed careful aim thing and flunked. 25 feet!, I could not believe it.
I am familiar with this. I was raised in a firearm family. I call it Zen shooting, Grandma called it “feeling” the bullet to the target, and Great Grand dad filed the front sights off all his revolvers.