I have a constable who is interested in instituting an automatic towing policy for all drivers cited for no DL or insurance. I have seen cities adopt ordinances for these types of practices, which leads me to believe that it's a little more complicated for counties. I've found Trans. Code 601.261 that addresses impoundment for second or subsequent convictions but nothing that would allow a constable to automatically tow the vehicle upon a ticket. Any thoughts?

Knowing your research skills to be top flight, my only observation (without the benefit of research) would be the basic tenet of county government law: If authority isn't provided to a county in the constitution or statutes, or isn't impliedly necessary to carry out an explicitly-stated duty, the county lacks such authority.