The Governor shall appoint heads for the various agencies listed in section 81-101, subject to confirmation by a majority vote of the members elected to the Legislature. Such appointments shall be submitted to the Legislature within sixty calendar days following the first Thursday after the first Tuesday in each odd-numbered year. The officers shall be designated as follows: (1) The Director of Agriculture for the Department of Agriculture; (2) the Commissioner of Labor for the Department of Labor; (3) the Director-State Engineer for the Department of Transportation; (4) the Director of Natural Resources for the Department of Natural Resources; (5) the Director of Banking and Finance for the Department of Banking and Finance; (6) the Director of Insurance for the Department of Insurance; (7) the Director of Motor Vehicles for the Department of Motor Vehicles; (8) the Director of Administrative Services for the Department of Administrative Services; (9) the Director of Correctional Services for the Department of Correctional Services; (10) the Director of Economic Development for the Department of Economic Development; (11) the Superintendent of Law Enforcement and Public Safety for the Nebraska State Patrol; (12) the Property Tax Administrator as the chief administrative officer of the property assessment division of the Department of Revenue; and (13) the chief executive officer for the Department of Health and Human Services. Whoever shall be so nominated by the Governor and shall fail to receive the number of votes requisite for confirmation, shall not be subject to nomination or appointment for this or any other appointive state office requiring confirmation by the Legislature during the period for which his or her appointment was sought. In case of a vacancy in any of such offices during the recess of the Legislature, the Governor shall make a temporary appointment until the next meeting of the Legislature, when he or she shall nominate some person to fill such office. Any person so nominated who is confirmed by the Legislature, shall hold his or her office during the remainder of the term if a specific term has been provided by law, otherwise during the pleasure of the Governor subject to the provisions of this section; except any such officers may be removed by the Governor pursuant to Article IV of the Constitution of Nebraska.