Ambidexterous Pitcher

[HugoTafurst]

8.01 (f) A pitcher must indicate visually to the umpire-in-chief, the batter and any runners the hand with which he intends to pitch, which may be done by wearing his glove on the other hand while touching the pitcher’s plate. The pitcher is not permitted to pitch with the other hand until the batter is retired, the batter becomes a runner, the inning ends, the batter is substituted for by a pinch-hitter or the pitcher incurs an injury. In the event a pitcher switches pitching hands during an at-bat because he has suffered an injury, the pitcher may not, for the remainder of the game, pitch with the hand from which he has switched. The pitcher shall not be given the opportunity to throw any preparatory pitches after switching pitching hands.
Any change of pitching hands must be indicated clearly to the umpire-in-chief.

Am I mistaken or isn't there also some guidance addresses the situation with a switch hitting batter?
Something that allows the pitcher to switch hands if the batter changes boxes, but only once?

A mind is a terrible thing to lose....