Both of these are treated like closely guarded, state secrets in South Florida. As much as folks love the ones from El Rey, El Mago, & Domino, the mystique of the special sauce and formulation of the patties in these places depart radically from traditional source recipes. I probably own every cookbook in Spanish or English printed over the past 30 years. Known enough aquaintances that I've asked over the past 45 years, and scoured the net to try an figure out the taste that I remember as a kid from the old Domino on 8th and 12th in my old barrio to what's morphed into the present day places. The home/classic recipes are sauced with nothing more then catsup, tomato paste, or in a few cases cocktail sauce that I've found mention on the net. Formulations for the patty vary from a sofrito base, beef, chorizio, milk,egg, and bread crumb mixture to everything in between. Yet the Fritas shops often include some form of special sauce on a non-chorizo base. BTW, I've tried Glenn's Special Sauce and have made it many times. It's certainly better then catsup, but otherwise not anything like these sauces that are both added during cooking and later as a condiment.
There appears to be some hints though. The patties have a decidedly high collagen texture as if either ground pork or gelatin are part of the mix although I seriously doubt gelatin and in some case doubt that chorizo isn't use, but that may be a recent development to hold cost down along with the now readily available smoked paprika as a foodservice shelf item. Just a hypothesis.
The sauces are intriguing. Most fritas are made behind closed kitchens with a window. Besides that, I never really paid attention to the texture. I was watching a video and noticed the way the sauce spillover during cooking was folded back onto the patty. Under heat, the coagulating sheeting suggests a protienaceous nature that may give a clue that the sauces are at part composed of a reduction that may have originally been part of pan juices or drippings. I can think of a possible suspect that would be available in copious amounts that would be otherwise discarded in a little corner cafeteria that might be the key.
I was hoping that someone might be able to validate the above observations or perhaps have some anecdotal information.