(a) The governor shall designate the chair of the commission from among the members of the commission. The chair shall serve in that capacity at the pleasure of the governor for a two-year term. The governor may redesignate the same member to serve consecutive terms.
(b) Notwithstanding Subsection (a), the member of the commission who represents the public shall serve as chair:
(1) when the commission acts under:
(A) Chapter 21;
(B) Subchapter D, Chapter 61;
(C) Subchapter D, Chapter 212;
(D) Chapter 301, Property Code; or
(E) Subchapter D, Chapter 51; and
(2) in commission hearings involving unemployment insurance issues regarding tax coverage, contributions, or reimbursements.