A first, I used to have both eyes open when shooting with my stylus epic (very small camera/viewfinder), but that habit is now present on my dslr/slr shooting aswell.
Specially when I shoot sports (bmx riding), I use 1/500 or 1/1000 shutter in order to stop the motion completely, and I use my left eye in the viewfinder to compose, but jus half a second before the moment of shooting is coming, I start paying attention to my right eye, the one seeing the actual scene, so I can press the shutter right when I want to, and this works for me 100%, EVERY TIME.
for example, handlebars exactly half way of the complete 360° rotation
https://farm6.staticflickr.com/5483/12090659995_67fa99a4c9_z.jpg
bike exactly half the rotation momentum
https://farm6.staticflickr.com/5480/10579054526_aae99ff7db_z.jpg
both eyes open works every time.