Learn to shoot with either hand, either eye, cross dominant eyes/hands and with both eyes open. For PP reasons, you must be able to respond to an attacker if you're injured so these capabilities are a must. When shooting in a PP situation, closing one eye is not a good idea. It destroys your peripheral view of the surrounding area. Bad guys hunt in packs. The one who confronts you may not be the one who will inflict the fatal attack. He may be approaching from the blind peripheral side.
When aiming with standard sights our hands and gun block the attackers body. Bad deeds come from hands and they're hidden by our own gun. And it's especially bad when one eye is closed. I prefer a laser sight on a PP gun. It allows me to maintain a clear line of vision by lowering the gun a few inches and keeping my peripheral view clear. Besides, that little red dancin' dot can be a deterrent the primary attacker's advance when checking your 3:00, 9:00 and 6:00.
Practice range exercises using both dominant and weak eyes. Eventually the weak eye will be just as accurate.