Google turned this up. Nothing on Texas, but I don't see it being different.
7.46.010 Gun dealer defined.
“Gun dealer” means any person, firm or corporation who sells or otherwise transfers to the public any pistol, revolver, rifle, shotgun, or other firearm, including those persons required by Section 12070(a) of the California Penal Code to obtain a license under California Penal Code Section 12071. “Gun dealer” also includes any person, firm or corporation who purchases, takes in trade or accepts on consignment from the public any firearm of any type, including, but not limited to pistols, revolvers, rifles and shotguns. (Ord. 97-0009 § 1, 1997: Ord. 91-0064 § 1 (part), 1991: Ord. 11282 § 1 (part), 1976: Ord. 5860 Ch. 2 Art. 19 § 760, 1951.)
I was in a consignment shop in South Carolina, and saw a Marlin 336 up with a price tag, and nothing indicating that this was a gun shop as well. I asked if the owner was an FFL, and he told me "No, that's my rifle, I'm not selling it for anyone else. When I sell it, it will be a face-to-face transaction." He probably bought it from someone wanting to put it on consignment, and went to sell it as his own. I always wondered if he wasn't asking for trouble or not.