Whenever the office of a Councilman shall become vacant, the vacancy shall be filled by a majority vote of all the remaining members of the Council and if the vacancy shall not be so filled within forty-five days, the Mayor shall fill it by appointment. Each Councilman so elected or appointed to fill a vacancy shall hold office for the balance of the unexpired term or until the beginning of the term of a successor elected for the unexpired term as hereinafter provided. A successor shall be elected for the unexpired term at the next Municipal election if:
(a) Such election shall occur more than two years prior to the expiration of the unexpired term, and
(b) The vacancy shall have occurred more than seventy-five (75) days prior to such election.