(a) The operator or owner of a vehicle is not required to unload any part of the vehicle's load under Section 621.403 or 621.404 if the vehicle is:
(1) a motor vehicle loaded with timber, pulp wood, or agricultural products in their natural state being transported from the place of production to the place of marketing or first processing; or
(2) a vehicle crossing a highway as provided by Subchapter C, Chapter 623.
(b) The operator of a motor vehicle may proceed to the vehicle's destination without unloading the vehicle as required by Section 621.403 or 621.404 if the vehicle is loaded with livestock.