In case of a vacancy on the council for any reason, the Mayor and Council, within 45 days, shall elect from the same ward in which the vacancy occurred some qualified person to fill such vacancy for the unexpired term. In case of a vacancy in the office of Mayor for any reason, the council within 45 days, shall elect some qualified person to fill the vacancy until the next regular town election. Any vacancies on the council or in the office of mayor shall be filled by the favorable votes of a majority of the remaining members of the Mayor and Council. The results of any such vote shall be recorded in the minutes of the council. In the event no one is appointed within the specified 45 day period, the Board of Election Supervisors for the Town will arrange for a special election.