Final answer:
A board member can be disqualified for not meeting required qualifications at the time of taking office or during service, ineligibility under specific sections, inability to discharge duties due to illness or significant absence without an approved excuse, or for involvement in insurrection as per Constitutional provisions.
Step-by-step explanation:
A member can be disqualified from serving on the board under several circumstances. If a member does not possess the qualifications required by Sections 201.051 and 201.052(b) at the time of taking office or does not maintain these qualifications during service, they can be disqualified. Additionally, a member can be disqualified if declared ineligible under Section 201.052 or 201.053, or if they are unable to discharge duties due to illness or disability for a substantial part of the term, or if the member is absent from more than half of the regularly scheduled board meetings without an approved excuse by the board's majority vote.
Furthermore, the House and Senate have the authority to judge the qualifications of their own members, as described in Section 5, Clause 1 of the Constitution. A majority presence is required for a quorum, which is needed to conduct business, and measures are in place to compel the attendance of absent members. This clause also implies that a member's positions and actions can be scrutinized, potentially leading to disqualification if they do not adhere to Constitutional guidelines, as noted in Section 3 where involvement in insurrection or rebellion disqualifies a person from holding office unless Congress removes this disability by a two-thirds vote.