Training to be a better instinctive shooter takes time. You can grasp the fundamentals of being an acceptable shooter in as little as a day, but without constant practice, you will most likely never be a good shooter. A trick to help make the transition may be just down the hall.
Dry fire and practice
Going as far back as Plato, and Aristotle, a phenomenon known as muscle memory or motor learning has been well documented. This is where you force a muscle group to do something so many times that the brain becomes used to it and basically can check out while the act is performed. Muscle memory thus becomes an unconscious process. Good examples of this are brushing your teeth, walking, and driving. It takes an estimated 1000 repetitions of an act to have even the beginnings of an adequate muscle memory for said act.
This means you have to work with your firearm in a basic draw-present motion 35 times in a row, 35 times, to have it *start* to become instinctive. Weapon out with a proper grip from contact and then extending your arms as you acquire your front sight is your primary motion to practice. Point firing from a one-armed, bent-elbow position is secondary but just as important. Both of these motions need a very high level of practice, but luckily, can be done from the safety of your own home.
The Mirror's Place
Jelly could get off a shot in under .040 seconds while drawing from a concealed carry position...after much practice.
Delf A." Jelly" Brycewas possibly one of the greatest modern gunfighters in law enforcement history. He was involved in no less than 19 police gunfights and came out on the winning end of each of them against some of the worst criminals and known cop-killers of the 1930s. Besides his own obvious natural talent, he honed his skills on relentless drawing and dry firing in front of a mirror. This showed Bryce how his entire body moved when he went to draw. By doing this, he could see what he needed to work on to trim those movements to the bare minimum. Smoothness is the key. Remember smooth is fast. Once you have the most efficient and balanced movement down pat, the speed will come with repetition of that movement. This is where the mirror is your guide to help in keeping your body in check.
When practicing at home in front of your mirror, safety is paramount. Be sure you have no brass and no live ammo of any sort in your magazines, firearm, pocket, chamber, cylinder, or for that matter, even in the same room. Most modern revolvers can be dry fired without issue; however, you should use snap-caps for automatics, even Glocks.
In the end if you ask, does the mirror work? Well, Jelly Byce died peacefully in his own bed at age 68 of natural causes.
I guess the guys he went up against didn't have that great of a mirror.