(a) A duly appointed senator's or representative's membership on the Legislative Budget Board, Legislative Library Board, Legislative Audit Committee, Texas Legislative Council, or any other interim committee terminates if the member:
(1) resigns the membership;
(2) ceases membership in the legislature for any reason; or
(3) fails to be nominated or elected to the legislature for the next term.
(b) A vacancy created under this section shall be immediately filled by appointment for the unexpired term in the same manner as the original appointment.
(c) If a member serves on the Legislative Budget Board, Legislative Library Board, or Legislative Audit Committee because of the member's position as chairman of a standing committee, this section does not affect the member's position as chairman of that standing committee.
(d) In filling a vacancy created under this section, the lieutenant governor or the speaker may appoint a senator or representative, as appropriate, other than a committee chairman designated by law to serve as a member of the Legislative Budget Board, Legislative Library Board, Legislative Audit Committee, Texas Legislative Council, or any other interim committee. An appointment made under this subsection does not constitute an appointment to any position other than that of a member of a board, council, or committee covered by this section.