Each officer whose office is created by the Civil Administrative Code of Illinois, except as otherwise specifically provided for in the Code, shall hold office for a term of 2 years from the third Monday in January of each odd-numbered year and until the officer’s successor is appointed and qualified. Where the provisions of the Code require General Assembly members to be included in the membership of any advisory and nonexecutive board, the General Assembly members shall serve such terms or until termination of their legislative service, whichever first occurs.