[greymule]

If as BR headed back toward 1B the pitcher went from making a play to standing in the circle (not necessarily on the rubber as in your post) without making a play, BR could indeed reverse direction and run toward 2B without violating the LBR. The fake cancelled everything that happened before it. We start anew when the pitcher ceases to be making a play. The runner is entitled to one stop/change of direction at that point.

If the BR does choose to reverse direction and run for 2B, she must stay in motion toward 2B until F1 makes a play.

If the BR was stopped when F1 ceased making a play, and then BR started back to 1B, she could not reverse direction or stop again.

Do not be misled by the POE (don't have the book with me) that says if the runner is in motion toward a base, she must continue toward that base. It's wrong.