In case any person duly elected an elector of President of the United States and Vice President of the United States shall fail to attend at the United States Capitol on the day on which his or her vote is required to be given, it shall be the duty of the electors of President and Vice President attending at the time and place to appoint persons to fill the vacancies. Should the person or persons chosen pursuant to this subchapter arrive at the place aforesaid before the votes for President and Vice President are actually given, the person or persons appointed to fill the vacancy shall not act as an elector of President and Vice President.