The term of office of the members of the committee who continue to be members of the senate and house shall be from the close of the session in which they were appointed or elected as provided in RCW 44.48.010 until the close of the next regular session during an odd-numbered year, or, in the event that such appointments or elections are not made, until the close of the next regular session during an odd-numbered year during which successors are appointed or elected. The term of office of such committee members as shall not continue to be members of the senate and house shall cease upon the convening of the next regular session of the legislature during an odd-numbered year after their confirmation, election, or appointment. Vacancies on the committee shall be filled by appointment by the remaining members. All such vacancies shall be filled from the same political party and from the same house as the member whose seat was vacated.