Chuck,
Once the pitcher breaks contact with the rubber he is a fielder. Pretty hard if not impossible to fake a throw to third without breaking contact with the pitching plate. On any throw from the rubber to a base he must step towards that base.
Re "having to throw to first": yes, if he is in contact with the rubber. If the pitcher properly disengages, he can throw or not throw as he sees fit, because now he's a fielder. In this case, faking the throw to third would fulfill the properly disengages part--as long as he steps towards third.
Dan
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