Notwithstanding the provisions of subsection (1) of section 60-6,119, when the Department of Transportation, any local authority, or its authorized representative or permittee has closed, in whole or in part, by barricade or otherwise, during repair or construction, any portion of any highway, the restrictions upon the use of such highway shall not apply to persons living along such closed highway or to persons who would need to travel such highway during the normal course of their operations if no other route of travel is available to such person, but extreme care shall be exercised by such persons on such highway.