Well I am quite sure you don't mean the actual oldest still running truck but rather enterprise. Raul Martinez the multi-million magnate of the King Taco empire claims to have opened the first taco truck in East LA in 1974 from a converted ice cream truck. Outside of El Taurino, he has a taco truck still operating--even though he owns the El Taurino restaurant itself, which is also a King Taco. Clearly Los Angeles is the birthplace of the taco truck . . . though whether you will credit Raul with the first title is up to you. I think he has one of the strongest claim to the modern taco truck, certainly extant taco truck.
Though a Lexis Nexis search will provide:
21 November 1966, New York (NY) Times, “From a Taste of a Taco, a New Shop” by Craig Claiborne, pg. 58:
"THE sign in the window says “Chile Today and Hot Tamale” and one of the owners, Mrs. Helen Swenson, explains that it’s only a joke. What they really sell are tacos and tortillas, and the name of this new establishment in Riverdale is Tic-Taco. And that’s no joke.
. . .
Out front there is a small yellow and orange TACO TRUCK [caps emphasis added] with a canopy fringed with cotton pompons. It travels about the neighborhood purveying the company product (there are visions of such taco trucks throughout Manhattan), and it is a part of the plan to rent the truck for parties. Complete, of course, with the tacos, fillings and so forth. The rental cost for a party, Mrs. Winslow explained, would be about $50.
Tic-Taco has been open for six weeks and customers started placing orders for New Year parties more than a month ago."
Certainly the Tic-Taco (by the way, Tic Tac Toe--some people I tell don't get it . . . the droll) owners saw the the taco truck trend before its time, though in California, such a taco truck trend must have been one of those things that too many people thought of and just never took the time to do the task . They didn't succeed in their enterprise as far as I know, and their taco trucks were certainly not the modern taco trucks--I am sure there were hand pushed trucks selling tacos well before the 20th century in Los Angeles.
2306 W 11th St, Los Angeles, CA 90006