A vacancy shall occur upon the death, resignation, removal from office (other than by recall) as authorized by law, or forfeiture of office of a Council member. A vacancy of the council shall be filled in one (1) of the following ways:
   (1)   If there are less than six (6) months remaining in the unexpired term or if there are less than six (6) months before the next regular Town election, the council, by a majority vote of the remaining members, shall choose a successor to serve until a newly elected council member is qualified. Notwithstanding any quorum requirements established herein, if at any time the membership of the council is reduced to less than a quorum, the remaining members may, by majority vote, appoint additional members under either [subsections] (1) or (2) [herein]. If one (1) year remains in the term of the vacated seat, at the time of the next regular election, that seat shall be filled by election for the remaining one (1) year;
   (2)   If there are more than six (6) months remaining in the unexpired term and no regular Town election is scheduled within six (6) months, the council shall fill the vacancy on an interim basis as provided in [subsection] (1), and shall schedule a special election to be held no sooner than sixty (60) days, nor more than ninety (90) days following the occurrence of the vacancy for the remainder of the initial term.
   In the event the office of Mayor is vacated, the Vice-Mayor assumes the position until a special election for the office of Mayor can be scheduled which election shall be held no sooner than sixty (60) days, nor more than ninety (90) days following the vacancy. During the period of time that the Vice Mayor is acting as Mayor, the Council will appoint a council member to fill the office of Councilman held by the Vice-Mayor. Once the position of Mayor is filled pursuant to the Special Election provided for herein, the Vice Mayor will reassume his duties as Vice Mayor and Councilman for the duration of his term of election.
   If the Council shall fail to fill a vacancy on the Council within thirty (30) days after it occurs, or whenever two (2) or more vacancies shall occur at the same time, the Mayor shall immediately call a special election to fill the vacancy or vacancies. Those elected at the special election will serve a term equal in time to what would have otherwise been the time remaining in the term of the Councilor-at-Large whose office has become vacant. Among the successful candidates those receiving the largest number of votes shall be declared elected for the longest terms.