No person shall be eligible for appointment to a hospital advisory board if he is a Member of the Legislature or an elective state officer, and if he becomes such after his appointment his office shall be vacated and a new appointment made. If any appointee fails to attend three consecutive regular meetings of the board, unless he is ill or absent from the state, his office becomes vacant, and the board, by resolution, shall so declare, and shall forthwith transmit a certified copy of such resolution to the Governor.