When I was little (late 60's), my family would go out to a large "Old School" Mexican restaurant (prob El Fenix) in N. Dallas Tx, and have exotic foods such as a combo plate, with cheese enchilada, crispy taco, tamale, and sides..
The dish had a Chili with meat (chili con carne) sauce on the enchilada and tamale. And as I seem to recall, even an extra little bowl of it on the side, which Dad promptly grabbed and poured over His..
Today, I don't see this Chili sauce often. Rather, it is usually a thin meatless gravy, like the one discussed here..
The essence of Tex-Mex | Homesick Texan
here is another discussion of the sauce from ChowHounds..
Chili Con Carne for Cheese Enchiladas? - Home Cooking - Chowhound
seems this fellow is looking for the same thing, but never really received a recipe..
It's really like thinned out Tx Red Chili, almost hot dog sauce thin..but not so "strong" to over power the taste of delicate cheese enchiladas, or Tamales..
Thanks, Eric Austin Tx.