The Vice-Mayor shall act as presiding officer of the Council in the absence or incapacity of the Mayor and during such absence or incapacity shall exercise all the powers and duties granted the Mayor by the Charter. While presiding over special or regular meetings of Council the Vice-Mayor may vote upon all matters coming before the Council, but in no event shall the Vice-Mayor in such person's dual capacity as Council member and presiding officer of Council, cast more than one vote on any action. In the event that the office of Mayor shall be come vacant, the Vice-Mayor shall become Mayor for the unexpired term, and Council shall elect a successor from among the membership of Council to the office of Vice-Mayor for that unexpired term.