This relay requires precision tuning. It is almost impossible to actuate it by hand and get the same precise results as a pulse from the game.
Your drive pawl is clicking more than one tooth on the drive gear when it is being pulsed by the game. IF you have adjusted everything else per the instructions, take apart the relay and check for wear at the hinge where the red arrow is pointing. Any wear on the frame or armature will cause inconsistent results even if the relay is adjusted per the instructions.
See wear on armature plate below. This little bit of wear caused the same condition as you describe and could not be compensated for by adjustment.
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