Section 11. As used in this section, the term “vacancy” includes a failure to elect. If a vacancy occurs in any town office, other than the office of selectman, town clerk, treasurer, collector of taxes or auditor, the selectmen shall in writing appoint a person to fill such vacancy. If there is a vacancy in a board consisting of two or more members, except a board whose members have been elected by proportional representation under chapter fifty-four A, the remaining members shall give written notice thereof, within one month of said vacancy, to the selectmen, who, with the remaining member or members of such board, shall, after one week’s notice, fill such vacancy by roll call vote. The selectmen shall fill such vacancy if such board fails to give said notice within the time herein specified. A majority of the votes of the officers entitled to vote shall be necessary to such election. The person so appointed or elected shall be a registered voter of the town and shall perform the duties of the office until the next annual meeting or until another is qualified.