(a) A person who fails to renew his license within two years after its expiration may not renew it pursuant to Section 724. Such person may apply and obtain a new license, in which case all of the provisions hereof shall apply as if such person were applying for a license for the first time.
(b) In the event a salesman’s license expires only because that salesman procured a broker’s license or a broker’s license expires only because that broker procured a salesman’s license, either former license may be reinstated under the provisions of Section 724 within two years of the expiration of the latter license.