(a) When a vacancy occurs in the office of council member in an incorporated town, at the first regular meeting after the occurrence of the vacancy, the town council shall elect by a majority vote of the town council a council member to serve for the unexpired term.
(b) When a vacancy occurs in the office of recorder-treasurer in an incorporated town, at the first regular meeting after the occurrence of the vacancy, the town council shall elect by a majority vote of the town council a recorder-treasurer to serve for the unexpired term.
(c) When a vacancy occurs in the office of mayor in an incorporated town, at the first regular meeting after the occurrence of the vacancy, the town council shall:
(1) Elect by a majority vote of the council members a mayor to serve the unexpired term; or
(2)
(A) Call for a special election to be held under § 7-11-101 et seq. to fill the vacancy.
(B) At the special election, a mayor shall be elected to complete the unexpired term.