The Stow-Munroe Falls Public Library is under the control and management of a board of library trustees consisting of seven (7) members. No one is eligible to membership on such board of library trustees who is or has been for a year previous to his appointment a member of the board of education making such appointment. A majority of such trustees shall be qualified electors of the school district, but a minority may be qualified electors of the county who reside outside the school district, and all shall be appointed by the board of education of the school district. All vacancies on such board of library trustees shall be filled by the board of education by appointment for any of the unexpired terms.