Any mechanic you'd like to add ???

[Dakota]

ASA allows the overhand out to be signalled with the left hand for left-handed umpires because the overhand out is a throwing motion. IOW, they recognize that a left-handed umpire "throws like a girl" with his/her right hand. (Apologies to our female colleagues and athletes - but you know what I mean.)

Perhaps the reason the "non-sell" out and strike "hammer" are not to be given with the left hand is to avoid confusion as to what the signal actually is. I agree that most of the time context should mean the possibility for confusion would be small...