Jeff,
It totally depends on the type of shooting/training you wish to do.
Im a Defensive pistol guy. Not skeet/trap/bullseye stuff.
Here is my take, based on 3 decades of teaching highend tactical pistol fighting at some of the major schools around the country. Teaching LE/Mil & Govt contract personnel.
First, you are not going to retrain eye dominance. Its a hardwired system, so we need to adapt our shooting style to our bodies NATURAL abilities.
Second, taping or patching the eye is a range only technique. No way to translate that into the real world.
So...As we bring the pistol to bear on target, the goal is to be as "neutral" as possible. For a right handed/right eye dominate shooter this is fairly easy. The gun favors the right side of centerline just a bit and everything lines up nicely.
For a right handed but LEFT eye dominate shooter, we need to cheat a little. But, only a LITTLE. Remember the eyes are NOT that far apart on humans. A cpl inches is all the difference we need to correct for, over the entire length of the arms (at extension)
Here is what i teach... As you extend the gun to tgt. Cheat the gun a little left, maybe just to centerline. As you do that TURN (dont TILT) your head slightly to the right. The difference is a TILT is ear towards shoulder, a turn is CHIN towards shoulder. You dont need much turn before the left eye is behind the sights. A few degrees is plenty.
The issue with tilting the head is it disrupts balance and thereby affects movement. Turning the head DOES NOT.
SO, gun to centerline...left eye to centerline and get to work on the trigger.
That has worked for a couple hundred cross dominant shooters ive had in my classes. All were able to quickly learn the subtle change in shooting style and were able to quickly get mtpl hits on tgtgs while on the move.
It WORKS