The plumbing board shall fix stated times and places of meeting, which times shall not be less than once each year, and meetings may be held more often upon written call of the chairperson of the board. The chairperson of the plumbing board shall also call a meeting of the plumbing board upon the written request of a license applicant, licensee, or another member of the plumbing board. Such meeting shall be held within four weeks of such written request. The plumbing board shall adopt and promulgate rules and regulations for the examination, at such times and places, of all persons who desire a license to work at the construction or repairing of plumbing within the city or village, and also within the area of the extraterritorial zoning jurisdiction of cities of the metropolitan class.