Notwithstanding the provisions of § 36-1-4, or of any other statute thereunto appertaining, a person who, while a member of the general assembly, is elected to office by the general assembly, or by either house thereof, or appointed to office by the governor, shall, within thirty (30) days after the date of his or her commission or within ten (10) days subsequent to the election and qualification of his or her successor as a member of the general assembly, whichever shall occur later, deliver to the secretary of state a certificate that he or she has been duly engaged thereon, signed by the person or persons before whom the engagement shall have been taken.