(A) If the number of vacancies on the Council is such that a quorum of the Council cannot be obtained, the Mayor shall appoint enough members to make a quorum and the Council shall then proceed to fill the remaining vacancies.
(B) If the number of vacancies on the Council is such that a quorum of the Council cannot be obtained and the Office of the Mayor is vacant, the Governor may fill the vacancies upon the request of any remaining member of the Council, or upon the petition of any five registered voters of the town.
(C) All vacancies that occur in any elective office of a town shall be filled by appointment of the Town Council for the remainder of the unexpired term.
(D) Vacancies in appointive offices shall be filled by the same authority that makes the initial appointment.