OBR Ambidexterous pitcher

[JJ]

I know from the OBR that if an ambidexterous pitcher faces a switch-hitter, the pitcher must declare with which hand he will pitch to that batter. My question is, can the batter then switch from one side to the other - and back again - during his at bat?

Here's the sitch - R1. The batter entered the box as a righty, and the pitcher switched the glove so he could throw as a righty. The umpire had the pitcher declare, and he declared "righty". The batter then switched to bad left-handed, ultimately to give R1 a better chance to steal with the left-handed batter doing his best to block the view of the catcher. The runner DID steal, and then the batter wanted to switch back to bat right-handed, which, as it turned out, was his natural side to hit from.

Input?

JJ