Left handed and left eye dominant guy here...new to USPSA, but I was pretty good at precision rifle (air and smallbore) and I wound up shooting a lot of right handed rifles over the years.
The big thing I noticed is that with my very strong left eye dominance, its just not possible to shoot with my right eye. Even with a blinder (tried a dozen colors and shapes), I just don't get a sight picture with my right eye. So it's left eye closed or don't bother.
So, go with your eyes. You can learn to point and press a trigger with your other hand, baring some handicap.
If you can't, when I have to shoot weak hand only strings, I just use something close to a precision air/free pistol stance and cant the gun just enough to get a sight picture with my strong eye. People have joked that they think I'm a righty in disguise....im new, so it's not amazing...but no worse than strong hand only. The groups are about the same.
Doing dry fire presentations from your chest can help get muscle memory for the angle, but only after you can do it free and strong hand. If you haven't done that yet, its freaky when it clicks....terms like "flash sight picture" and "fuzzy target AMD rear, clean front sight" make a lot more sense once you've seen them for yourself. And, yes, they mean fuzzy target, not fuzzy targets.
sent from a device without a real keyboard, sorry for things that don't make sense.