The City Administrator shall be appointed by the majority vote of the Council and shall hold office at the pleasure of the Council. During the Administrator’s tenure of office, said Administrator must reside within the City limits. The appointee for the position of City Administrator does not need to reside within this area at the time of the appointment, but must meet this requirement within sixty (60) days after the first day of employment with the City. No Council member shall receive such appointment during the term for which the Council member has been elected or within one year after the expiration of the Council member’s term.