I always turn, facing aft, and switch sides quickly, passing the tiller from one hand to the other.
As far as taking your eyes off of things during a critical maneuver....well, it literally takes me 1 second or less to make the switch. Not a factor.
If I was ever in a situation where a 1 second (or less) loss of forward vision could cause a problem....I'd just complete the tack, trim up....then switch sides when it's safe to do so. I do prefer to sail on the high side since I can see better and pull the tiller to me rather than push it away, but I can sail from either side.
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1982 Catalina 25 #2897
Eagle Mountain Lake, Texas