+1 for practicing with both eyes open while dry firing. When I first started shooting pistols I felt like I had to close my non-dominant eye to get a good sight picture. However, I realized some time ago during a range session that I was shooting with both eyes open. I don't remember consciously transitioning. I think the transition occurred when I started focusing on the front sight during practice sessions. My accuracy improved dramatically and I found that when I consciously focused on the front sight that I naturally used my dominant eye to focus and was able to do that with both eyes open. Now when I shoot, my focus is on the front sight and the back sights, target and surroundings are visible, but don't distract my focus away from the front sight even with both eyes open. Also, keeping both eyes open and focusing on the front sight reduces the "wobble" that you perceive when aiming the pistol. If you shoot with only one eye open, you really notice the wobble and start fighting it, which will cause you to try to time the break and will lead to anticipating the recoil.
I'm probably not explaining this well, but try dry firing with both eyes open and with your focus on the front sight and I think that you'll see what I mean. Don't just "see" the front sight, make sure that the front sight is your point of focus. If you practice it enough, it will start to come naturally.