The term of office of Cemetery Trustees, beginning on the first Monday in May, shall be three years. Whenever a position on the Cemetery Board becomes vacant, the Mayor and Councilors shall proceed to fill the position in accordance with Section 3.6(e) of this Charter. The Clerk-Treasurer shall publicize all vacancies and solicit applicants through both public notices and newspaper advertisements or in a municipal newsletter if one is published and distributed throughout the city during a period prior to a person’s being nominated to fill such a vacancy.