Any person not licensed under this article or lawfully operating as a nonresident under this article, convicted of a violation for which suspension or revocation of driver’s license or privilege to operate is made mandatory, who shall thereafter operate a motor vehicle in this State before such time as he obtains a driver’s license from the Department of Motor Vehicles or until the Department shall find that he is properly qualified to operate as a nonresident, shall be punished by a fine of one hundred dollars or imprisonment for thirty days, and the period of time during which the Department may not issue to him a driver’s license or find that he is properly qualified to operate as a nonresident shall be extended as provided in § 56-1-460. Such license shall not be issued nor shall such findings be made until the lapse of the period of time counting from the date of conviction during which such person’s license would have been subject to suspension or revocation had he been properly licensed at the time of such offense.