B. Notwithstanding the provisions of § 46.2-1013 or 46.2-1014, any trailer or semitrailer exempt from registration pursuant to § 46.2-665, 46.2-666, 46.2-670, 46.2-672, or 46.2-673 may be operated without tail lights or brake lights on the highways of the Commonwealth located in Planning Districts 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, and 23, except interstate highways, between sunrise and sunset, provided that such trailer or semitrailer has affixed to the rear end either (i) two or more reflectors of a type approved by the Superintendent or (ii) at least 100 square inches of solid reflectorized material. Such a trailer or semitrailer operated without tail lights or brake lights shall keep to the rightmost lane when operating on such a highway, except when turning at an intersection or avoiding any hazard. However, any such trailer or semitrailer operated without tail lights or brake lights shall not be operated on the highways of the Commonwealth (a) during any time when, because of rain, smoke, fog, snow, sleet, insufficient light, or other unfavorable atmospheric conditions, visibility is reduced to a degree whereby persons or vehicles on the highway are not clearly discernible at a distance of 500 feet or (b) whenever windshield wipers are in use as a result of fog, rain, sleet, or snow.