In case any person duly elected an elector of President and Vice-President of the United States shall fail to attend at the Capitol on the day on which his vote is required to be given, it shall be the duty of the elector or electors of President and Vice-President, attending at the time and place, to appoint a person or persons to fill such vacancy; provided, that should the person or persons chosen, as in this Article provided, in the foregoing sections, arrive at the place aforesaid before the votes for President and Vice-President are actually given, the person or persons appointed to fill such vacancy shall not act as elector of President and Vice-President.