I can tell you that when I grew up in the Coastal Bend area, the barbecue was a cross-over between barbacoa style, and what we know as pit roasted, in brick or block pits. I have more memories of backyard cooking in the 60's, and most of it was driven by cost. Chicken, brisket and goat was cheap in those days, so that's what folks cooked. We did have our own beef butchered....they opted for steaks, round steaks and sirloin steaks, so all the roasts came from the front end. The "Bar-B-Que" stands might have served some pork, but I don't recall ever having any,... they all served sausage, and the beef was just called beef, it was always sliced... not saucy BBQ beef or anything. You could get white bread, tortillas or saltine crackers, and either a jalapeno or a pickle, and of course every stand had beans. The seats were mostly all outside under an awning, or you just bought it to go.
In the Hill Country, most of the Mexican influence was gone. We called places up there joints, not stands, because you could go inside to sit. The sausages had different flavors, and I don't remember pork in those joints either, just sausage and beef. I remember the meats were more bland, not in a bad way.... just no chile powder or hot pepper spices. However the meats had more smoke flavor. Pickles were really common, and the food came with bread or crackers.
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Barbecue is not rocket surgery