I'll agree with your assumption that the PU may not see the OBS as he is focusing on the ball near the base line. However, the BU is 70+ feet away with a wide view of the whole thing. The BU should be able to pick up the OBS on the BR going to first base.
Also, the BU should not be "moving in" for two reasons:
a) you have a runner going from first to second in front of you
b) from a proper B position you have a good angle on a play at either first or second. Once the fielder gets to the ball, let the play take you to one base or the other.
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