Sec. 20. (a) A library board member may be removed at any time by the appointing authority, after public hearing, for any cause:
(1) that interferes with the proper discharge of the member's duties as a member of the board; or
(2) that jeopardizes public confidence in the member.
(b) A vacancy occurs whenever a member is absent from six (6) consecutive regular board meetings for any cause other than illness. The appointing authority shall be notified by the secretary of the board of a vacancy.