The governor shall appoint four members of the board of trustees of the Ohioana Library Association, Martha Kinney Cooper Memorial. Terms of office shall be for four years, commencing on the sixteenth day of September and ending on the fifteenth day of September. Each member shall hold office from the date of appointment until the end of the term for which appointed. Any member appointed to fill a vacancy occurring prior to the expiration of the term for which the member’s predecessor was appointed shall hold office for the remainder of that term. Any member shall continue in office subsequent to the expiration date of the member’s term until the member’s successor takes office, or until a period of sixty days has elapsed, whichever occurs first. The gubernatorial appointees shall serve as members of the board of trustees in addition to the regular constituted board of trustees of the corporation.