If the office of Mayor becomes vacant, the President of Council shall forthwith become Mayor for the unexpired term and the Vice President of Council shall become President of Council. Thereupon, the vacancy in Council shall be first filled in the manner provided hereinafter and, thereafter, a new Vice President of Council shall be chosen by Council. If the President of Council declines to serve as Mayor, Council shall then appoint, by a majority vote, one of its members as Mayor for the unexpired term. If a Mayor-elect fails to qualify for office, a vacancy shall be deemed to exist and the President of Council elected at the organizational meeting following such regular municipal election shall become Mayor for that term as provided above.