(a) Any vacancy which occurs in the office of mayor or in the council shall be filled within thirty days by a majority vote of the remaining members of the council. Said vacancy shall be filled for the balance of the unexpired term.
(b) Any vacancy which occurs in the office of municipal judge shall be filled within thirty days by a majority vote of the council. Said appointment shall be filled for the balance of the unexpired term.
(c) If any vacancy in the office of mayor, councilman, or municipal judge is not filled by the council as required by subsection (a) or (b), or if the number of vacancies existing in the council is such as to reduce the membership below a quorum, the clerk shall, forthwith, call a special city election for the purpose of filling such vacancy or vacancies for the balance of the term or terms thereof. Such election shall be held not less than forty-five days nor more than sixty days after the date of the call thereof by the clerk. Each such election shall be governed by the provisions of this charter, except that no primary election shall be held in connection therewith and the last day and time for filing nominating petitions in connection therewith shall be at 5:00 p.m. on the 30th day before the date of such election. The qualified person or persons receiving the highest number of votes cast at such election shall be deemed to have been elected to fill the vacancy or vacancies, as the case may be, to be filled at such election and, upon canvass of the votes cast at such election, shall be certified as such, subject to the provisions of law.
(d) The provisions of this section shall not apply to the filling of vacancies resulting from recall.