Rule sets / NCAA / Illegal Feint Balk
It varies by rule set but feints to first base are generally prohibited and a feight to third base might be as well.
If there is a runner or runners, a balk shall be called for the following action by a pitcher: While touching the pitcher’s plate, any feinting motion without completing the throw toward the batter or toward first or third base.
TODO: describe the Illegal Feint Balk in plain English.
TODO: explain the rationale — what the rule is protecting against.
TODO: what the pitcher should do differently.