The board from time to time, may adopt, amend and enforce rules and regulations in accordance with Act No. 88 of the Public Acts of 1943, as amended, being section 24.71 to 24.82 of the Compiled Laws of 1948, and subject to Act No. 197 of 1952, as amended, being section 24.101 to 24.110 of the Compiled Laws of 1948, necessary or desirable in carrying out the provisions of this act. The board may require owners and operators of foreign registered vehicles claiming exemptions or privileges under compacts, agreements, arrangements or declarations authorized by this act, to supply lists of vehicles for which exemptions and privileges are requested and to require the vehicles to display a reciprocity plate or other identification prescribed by the board, as a prerequisite to the enjoyment of the exemptions and privileges claimed thereof.