Thanks all.
The pitcher's actions were not a feint. I believe she was preparing to make a throw to 2nd as the BR advanced.
In the FED rule 8-7-3a it says: Responsibilities of the BR after completing a turn at bat, and while the pitcher has the ball within the 16-foot pitching circle, including a base on balls... are:
a. a BR who rounds first base toward second base may stop, but then must immediately return to first or attempt to advance non-stop to second base;
EXCEPTION: The runner will not be declared out if a play is made on
another runner, (a fake throw is considered a play), the pitcher no longer has possession of the ball within the 16-foot circle, ....
So where is the rule/instruction about making a feint toward the batter runner (that I seem to recall - perhaps ASA)? The FED exception specifically states "another," as in different (like R3), runner. Does this mean the pitcher COULD make a feint at the BR and the out still called? For some reason my gut feeling is,(and given your answers), that No, F1 cannot make a feint at the BR. But I don't see it supported in the FED rules.
Perhaps my memory is that F1 does not need to make any feint or attempt at a play if the BR is standing, doing a little face-off thing with the pitcher and not making a movement towards either base. Umpire should declare an out.
I appreciate your help.