In answer to the OP's original question, most instructors will try to switch either your eye or the dominant shooting hand so you use the same side hand and eye for pistol. It's "easier" for the instructor to figure out problems and, more importantly, correct them so you shoot better. It's great if it works but obviously has limitations if it doesn't.

I've seen some shooters who could transition to same eye/hand and some who simply could not. The trick is to figure out what the shooter can live with and then help them perfect their technique and skill sets with that method.