(a) An employee of the public school system is not permitted to be a member of the retirement system if the employee:
(1) is eligible and elects to participate in the optional retirement program under Chapter 830; or
(2) has retired under the retirement system and has not been reinstated to membership pursuant to Section 824.005 or 824.307.
(b) An employee of a public institution of higher education who is required to be enrolled as a student in the institution as a condition of employment is not permitted to be a member of the retirement system based on that student employment, and compensation paid to the employee for work performed as a student employee is not compensation subject to report and deduction for member contributions or to credit in benefit computations under Section 822.201.