Where a vacancy on a board of trustees of a college or university of this State, requiring election by the General Assembly to fill, has occurred for any reason other than expiration of the term and is unfilled at the beginning of an annual session of the General Assembly, a joint review committee to consider applicants for this vacancy and others of similar circumstances must be appointed within six legislative days after the annual session of the General Assembly convenes, and the election to fill this vacancy must occur within six weeks after the joint review committee is appointed unless no candidates for the office are offering for election who have been reviewed by the committee.