When the governor-elect shall die, remove from the state, refuse to serve; become insane, or be otherwise incapacitated, the lieutenant governor-elect shall be qualified as governor at the beginning of the term for which the governor was elected. When both the governor and lieutenant governor-elect, or either the lieutenant governor, secretary of state, attorney-general, or general treasurer-elect, are so incapacitated, or when there has been a failure to elect any one or more of the officers mentioned in this section, the general assembly shall upon its organization meet in grand committee and elect some person or persons to fill the office or offices, as the case may be, for which such incapacity exists or as to which such failure to elect occurred. When the general assembly shall elect any of said officers because of the failure of any person to receive a plurality of the votes cast, the election in each case shall be made from the persons who received the same and largest number of votes.