The rule has been significantly expanded in detail. I have a 2004 PBUC manual and a 2007 MLBUM. The 2007 MLBUM doesn't address ambidextrous pitchers. The 2004 PBUC manual includes only the portion in italics below:

• The pitcher must visually indicate to the umpire, batter and runner(s) which way he will begin pitching to the batter. Engaging the rubber with the glove on a particular hand is considered a definitive commitment to which arm he will throw with. The batter will then choose which side of the plate he will bat from.
• The pitcher must throw one pitch to the batter before any "switch" by either player is allowed.
• After one pitch is thrown, the pitcher and batter may each change positions one time per at-bat. For example, if the pitcher changes from right-handed to left-handed and the batter then changes batter's boxes, each player must remain that way for the duration of that at-bat (unless the offensive team substitutes a pinch hitter, and then each player may again "switch" one time).
• Any switch (by either the pitcher or the batter) must be clearly indicated to the umpire.
• There will be no warm-up pitches during the change of arms.
• If an injury occurs the pitcher may change arms but not use that arm again during the remainder of the game."

The first paragraph puts an end to any stalemate before the first pitch is thrown. And they added rules to cover other possible situations.

The hitter should dictate first...typically that's how pitching changes are made. That would seem fair to me...I haven't really looked at this particular rule too much...

Just got my 2009 MLB rules though...and I did see it in the Index.

But in this case it appears as though the pitcher dictates...there aren't that many switch hitters anyway so more often than not, the dictating isn't going to be a huge issue.

Lame, John. Lame. ;)

FED and NCAA have "always" addresses this -- and the pitcher must declare first.

And, since there are far more sitch-hitters than abidextrous pitchers, it's consistent with that -- the "normal" pitcher "declares" (since he has no practical choice) and then the switch hitter chooses the side of the plate. If there's a pitching chage, the hitter can change sides.