<font size="1" face="TTE595CF58t00"><font size="1" face="TTE595CF58t00"><p align="left">f) A pitcher must indicate visually to the umpire-in-chief, the batter and any runners</p><p align="left">the hand with which he intends to pitch, which may be done by wearing his glove</p><p align="left">on the other hand while touching the pitcher’s plate. The pitcher is not permitted</p><p align="left">to pitch with the other hand until the batter is retired, the batter becomes a runner,</p><p align="left">the inning ends, the batter is substituted for by a pinch-hitter or the pitcher incurs</p><p align="left">an injury. In the event a pitcher switches pitching hands during an at-bat because</p><p align="left">he has suffered an injury, the pitcher may not, for the remainder of the game,</p><p align="left">pitch with the hand from which he has switched. The pitcher shall not be given</p><p align="left">the opportunity to throw any preparatory pitches after switching pitching hands.</p>
Any change of pitching hands must be indicated clearly to the umpire-in-chief.
</p></font></font>I haven't looked, but i assume there's no rule forbidding the hitter from switching sides of the plate within an atbat. So the pitcher must declare his side, and the batter can then choose. Advantage for switch hitters, but advantage to the switch pitcher against the rest.