Long ago I taught pistol craft. My students were taught that a handgun would always wiggle on and off target. With practice this wiggle would become sort of a "circle" (and get smaller and smaller) and this was preferred. Trying to hold steady on a fixed point is exceedingly difficult and impossible for most of us. This way most rounds would fall into a regular pattern around the bulls eye and get tighter with practice.
That "wiggle" is what the Marine Corps calls your "natural wobble area." By using a lot of dry firing practice, one strengthens the muscles needed to hold the rifle or pistol more steady and that lessens the wobble area or the amount of wiggle off target. Dry firing also teaches you to pull smoothly and hold the rifle smoothly as the cock or hammer falls and the rifle goes off. You still keep aiming and holding until "the ball has had a chance to hit the target." That ensures you have good follow through.
You can also lessen the wobble area by establishing a natural point of aim by positioning your body and feet so that when you bring the rifle up to where it "feels" right, you should be looking straight in the center of what you are shooting at. You check that by closing your eyes and bring the rifle up. Then open your eyes and see how far off the mark you are. You then move your feet and try it again until when you open your eyes, the sights are centered. While it may sound complicated, it takes less than a minute to establish the natural point of aim for off hand shooting.
I spent 23 of my 26 years on active duty around some of the finest shooters in the world. Only one or two of the best could "make the gun go off" by deliberate will when they got it in the center of the target. Most folks trying that wind up flinching the shot off center and that includes National, International and Olympic competition.
What the overwhelming majority of the best shots say is to "accept your wobble area" and pull smoothly on the trigger while keeping the front and rear sights absolutely aligned as perfectly as possible. Don't worry as you wobble in and out of your natural wobble area that the front sight won't be perfectly aligned at all times and let the rifle go off when it does naturally. Keeps you from flinching or jerking a shot off call.
The only thing you should do when using this method is that if it takes so long for the shot to go off, it is better to take the rifle out of your shoulder and take a couple of breaths and start again. If you try to force the shot after holding it up too long, it is almost sure to be a flyer.
I'm not a world class shot by any means, though I did tie 8 other Marines in history by shooting a 249 out of 250 on the Re qualification Range at Quantico. I don't know exactly when they established the Rifle Range at Quantico, but I think it was in the 1930's. I was the ninth Marine to fire a 249 and no one had fired a 250 when I retired in 1997.
I had shot expert with the pistol maybe seven times when I went through the NRA Police Firearms Instructor Course. You have to shoot 90 Percent scores with the pistol and shotgun and get at least 90 percent on the final exam to pass that course. I had only "just" made expert with the pistol each time before graduating that course, though by maybe only 10 to 15 points. For whatever reason, "the lights finally came on" about perfect alignment of sights and accepting my wobble area, etc. and from then on - I always fired high Expert with pistol as well. It also helped me to Tie the "All Time Record" with the rifle mentioned earlier. I finished my career with 13th Rifle Expert award and always fired Expert with pistol to make that a straight run of 12 Expert awards.
I would this technique to instruct my young Armorers on shooting the pistol before they went to qualify. Many of them had never fired a pistol for more than maybe 5 or 10 rounds of "familiarization fire," prior to qualifying. I ran an average of about 75 % of even those Armorers firing expert using these techniques.
BTW, it doesn't matter whether the rifle or pistol is a Matchlock or the most modern super duper whatchamacallit, these techniques work on all of them.