In case of a vacancy in the office of the governor, president of the senate, speaker of the house of representatives, the majority or minority floor leader of the senate, or the majority or minority floor leader of the house of representatives, such officers successor shall be a member of the finance council. In the event of a vacancy in the council in case of:

(a) The chairperson of the senate committee on ways and means, the president of the senate shall appoint a successor from the membership of such committee; and

(b) the chairperson of the house of representatives committee on appropriations, the speaker of the house shall appoint a successor from the membership of such committee.