The term of office of the members of the joint committee shall be two years, ending two years from the date of appointment or when a member is no longer a member of the house from which he or she was appointed, except that members shall continue to serve until a successor is appointed. Vacancies on the joint committee shall be filled from the same political party and from the same house as the member whose seat was vacated. Senate vacancies shall be filled through appointment by the president of the senate, and house vacancies shall be filled through appointment by the speaker of the house.