The principal office and place of business of the board of joint control shall be at a place to be designated by the board in the county in which the board was created. Each member of the board before entering on the duties of his or her office shall subscribe a written oath for the faithful discharge of his or her duties as a member and file the oath with the county clerk of the county. The filing of the oath shall be without clerk's fee. The term of office of members of the board is for one year or a fraction thereof ending on the first Monday in March next following their selection and until their respective successors are selected as provided in this section. The term of the first members of the board shall also be as above stated. In January of each year the board of directors of each irrigation entity concerned shall designate in writing and deliver to the board of joint control, the name or names of the person or persons who constitute the entity's membership and who shall represent the entity on the board of joint control for the ensuing year. The persons designated under this section constitute the board of joint control for the year and until their respective successors are selected and have qualified. Any irrigation entity that fails to designate its representative and to file the same as provided in this section is not entitled to representation on the board unless and until the requirements are complied with.