In every such city or town there shall be a board of plumbing examiners, consisting of three members, one of whom shall be the health officer of the city or town, who shall be ex officio the chairman of such board. The second member of such board shall be a master plumber with not less than four years’ experience and the third member shall be a journeyman plumber, with not less than four years’ experience. Such second and third members of such board shall be appointed by the mayor of the city, if such city has a mayor and, if not, then by the governing body of such city or town. Each of such appointees shall hold office for the term of one year and until his successor is appointed as herein provided for. Upon the expiration of any term of office of such second and third member of any such board, his successor shall be appointed by the mayor or governing body, as hereinbefore provided and such successor shall hold office for the term of one year and until his successor is appointed. In the event of a vacancy on the board, caused by the death, resignation or removal from office of the second or third member, such vacancy shall be filled by appointment of such mayor or governing body as hereinbefore provided and such appointee shall hold office for the unexpired term of his predecessor.