Whenever a dispute exists concerning wages, hours of labor, or conditions of employment of members of a paid fire department of any county, city, town, fire district, or other governmental unit having a population in excess of twenty thousand or located in a county of the first class, and a request for arbitration is made by either party to the dispute, a firemen’s arbitration board shall be appointed as provided in sections 290.350 to 290.380. Request for arbitration may be made by written petition signed by at least fifty-one percent of the employees of the fire department or by resolution of the county commission, council, board, or other governing body having direction and control over the fire department.