(a) Except as provided by Subsection (c), a retiree may not rejoin the retirement system as a member of the class from which the person retired.
(b) A retiree who takes a position not included in a membership class from which the retiree receives retirement benefit payments:
(1) is required to become or remain a member if the position is included in the employee class; or
(2) may elect to become or remain a member if the position is included in the elected class.
(c) A person who is retired from the elected class of membership and who again holds a position included in that class may elect to become a member again by filing notice with the retirement system. Except as provided by Section 812.203(c), when benefit payments are resumed, the retirement system shall recompute the annuity selected at the time of the person's original retirement to include the additional service established during membership under this subsection.