Depends on what u are calling south texas
That region covers a lot of territory but generally you can draw a line anything south of hwy 90 and bordering those eastern counties along the coast.
You'll get a lot of arguements but that is just speaking in general terms.
The rut usually starts around Thanksgiving along the northern part closer to hwy 90, and the more south you go it gets later as around Christmas and on into January in deep south Texas.
The rut is close, but yet to come in most of south Texas.