The civil service board shall make rules and regulations to carry out the purpose of this article, and for examinations, appointments, and removals in accordance with its provisions and the board, from time to time, may make changes in the existing rules. The chief of police and the chief of the fire department, from the membership of their respective departments, shall recommend for promotion such person or persons as the occasion may call for to fill any vacancy or vacancies that may occur in the respective departments, and all such vacancies shall be filled and all such promotions shall be made by the civil service board. The board may make rules and regulations relating to the eligibility for promotion. The chief of the police department and the chief of the fire department shall have authority in their respective departments to demote any member of the respective departments by and with the consent and approval of the civil service board, provided however, that upon written demand filed with the civil service board within five days from the date of the order of demotion the person whom it is proposed to demote shall be given a public hearing by the civil service board before any order of demotion shall be final. The chief of the police department and the chief of the fire department shall have authority to suspend any member of their respective departments pending the hearing by the civil service board. In the event any vacancy shall occur in the office of chief of the police department or chief of the fire department such vacancy shall be filled by the civil service board. In the event there is a reduction in the number of firemen or policemen employed by the city, the person last employed shall be the first to be dropped, and so on in succession; provided that the number of patrolmen in the police department who are qualified as motorcycle patrolmen shall not thereby be reduced below the number which may from time to time be determined by the board of commissioners of the city as needed for motorcycle patrolmen; provided, further, that the number of persons in the fire department who are qualified as mechanics shall not thereby be reduced below the number which may from time to time be determined by the board of commissioners of the city as needed for mechanics in the department. The civil service board may at any time, upon the request of the governing authority of the City of Florence, shown by resolution, discharge from employment the chief of police and the chief of the fire department or any number of either the police or fire departments.