The Vice Mayor, during any period when the Mayor shall be absent or unavailable or unable for any cause to perform his duties, shall be the Acting Mayor and shall also continue as a councilman with all the powers and duties of a councilman. In case the office of Mayor shall become vacant, the Vice Mayor shall thereupon become Mayor, and his office as councilman shall become vacant, and he shall serve as Mayor for the unexpired term; and if both the office of Mayor and the office of Vice Mayor shall become vacant at the same time, the Council shall elect a Vice Mayor who shall thereupon become Mayor. When temporarily the Vice Mayor is absent or inaccessible or for any reason unable to perform his duties as Acting Mayor, then Council by a vote of a majority of the remaining members of Council shall designate one of their members to act as Mayor; but such member shall continue as a councilman with all the powers and duties of a councilman.