A board, to be known as the Board of Barber Examiners, is hereby established, to consist of three members appointed by the Governor. Each member shall be a practicing barber who has followed the occupation of barbering in this state for at least five years prior to his appointment, and who is actually engaged in the practice of barbering during the term of his appointment. The members of the first board appointed shall serve for three years, two years, and one year, respectively, as appointed, and members appointed thereafter shall serve for three years. The Governor may remove a member for cause. Members appointed to fill vacancies caused by death, resignation or removal, shall serve during the unexpired term of their predecessors.