Each house of the Legislature shall, at the commencement of the regular session thereof assembled and held in odd-numbered years, elect a presiding officer, a clerk, a sergeant-at-arms and a doorkeeper, whose terms of office shall, unless sooner vacated by death, resignation or removal, be and continue until the regular meeting of the Legislature in the odd-numbered year next thereafter, and until their successors are elected and qualified. Any person who is an officer of any state, county, district or municipal political party executive committee shall not be eligible to serve as clerk of either house of the Legislature. The clerk of each house shall devote full time to his public duties to the exclusion of any other employment. At each session of the Legislature, there shall be appointed for each house such employees and technical assistants as may be authorized by law or by resolution of the respective houses. Any person so appointed may be removed by the appointing authority and another appointed in his stead: Provided, That nothing in this section shall be construed to prevent either house from removing any appointee.