(f) In the event a dispute arises as to the right of any national labor organization to participate as per paragraph (c) of this section in the selection and designation of the labor members of the Adjustment Board, the Secretary of Labor shall investigate the claim of such labor organization to participate, and if such claim in the judgment of the Secretary of Labor has merit, the secretary shall notify the Mediation Board accordingly, and within 10 days after receipt of such advice the Mediation Board shall request those national labor organizations duly qualified as per paragraph (c) of this section to participate in the selection and designation of the labor members of the Adjustment Board to select a representative. Such representatives, together with a representative likewise designated by the claimant, and a third or neutral party designated by the Mediation Board, constituting a board of three, shall within 30 days after the appointment of the neutral member investigate the claims of the labor organization desiring participation and decide whether or not it was organized in accordance with section 2, hereof, and is otherwise properly qualified to participate in the selection of the labor members of the Adjustment Board, and the findings of such boards of three shall be final and binding.