No member of the legislative delegation of Richland County shall be eligible to appointment to membership on the board of Columbia township auditorium, the venereal clinic or on any such like organization or board of the county or of Columbia township receiving financial aid from the county or township. All vacancies from time to time occurring in the membership of any such board, which it is provided by law shall be filled by the county legislative delegation, shall be filled by a majority vote of the delegation.