In the event of death, disability, resignation, or ineligibility of a board member who is a state employee, the board of trustees is authorized to appoint a member from the group represented by the deceased or resigned member to fill the member's unexpired term. In the event of the death, disability, resignation, or ineligibility of a board member who was appointed as teacher trustee or the retired teacher trustee, the speaker of the senate or the speaker of the house of representatives who appointed the member shall appoint a trustee to fill the member's unexpired term.