The Governor shall, subject to confirmation by the Senate, appoint an executive director of the agency, who shall, subject solely to supervision by the board, administer and direct the day-to-day operations of the agency. The term of office of the executive director is five years. Except as provided in this part, the board shall from time to time determine the total number of authorized employees within the agency and shall determine the salaries of those employees of the agency whose salaries are not paid from moneys appropriated to the agency from the General Fund.