“Pico de gallo” is a Mexican food, but probably more Cal-Mex than Tex-Mex. I pointed this dish out to the OED and supplied the 1962 citation below.
   
     
Wikipedia: Pico de gallo
In Mexican cuisine, pico de gallo (Spanish pronunciation: [ˈpiko ðe ˈɣaʎo], lit. beak of rooster), also called salsa fresca or salsa cruda, is traditionally made from chopped tomato, onion, and cilantro, with lime juice mixed in.
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Etymology
According to food writer Sharon Tyler Herbst, pico de gallo (“rooster’s beak”) is named thus because originally people ate it by pinching pieces between the thumb and forefinger.
 
In their book Authentic Mexican: Regional Cooking from the Heart of Mexico, Rick Bayless and Deann Groen speculate that the name might allude to the bird feed-like texture and appearance of the mince.
 
Many native residents of the Sonoran Mexico region explain that the salsa is thus named because the serrano pepper resembles a rooster’s beak in shape.
 
(Oxford English Dictionary)
pico de gallo, n.
Chiefly U.S.
[< Mexican Spanish pico de gallo a spicy Mexican relish, lit. ‘cockerel’s beak’ < Spanish pico (see PICO- comb. form) + de DE prep. + gallo cockerel (1207; < classical Latin

gallus: see GALLINE adj.).
It is uncertain why the Spanish phrase should be used in this sense; one suggested explanation is that this is due to the heat of the dish creating a painful sensation on the tongue, similar to being pecked by a bird.] 
A Mexican salsa or salad, typically made with coarsely chopped tomatoes, onions, lemon juice, chillies, and coriander, and served as an accompaniment.
1958 Independent Star-News (Pasadena, Calif.) 23 Feb. (Scene section) 29   Ponder this near-fatal event and its historical repercussions over a tequila chased by a ‘pico de gallo’ (orange, jicama fruit and small, red and hot chile pepper) and the stern stuff of the Mexican Revolution will seem real.
1962 Los Angeles Times 7 Oct. e17/1 (heading)  Pico de Gallo (Comb of the Rooster).
1970 Pomona (Calif.) Progress-Bull. 20 Feb. B3/5 Mexican fried rice, orange and cucumber salad called pico de gallo, and lemonade.
1991 Food & Wine Aug. 79/1 With the addition of cilantro, it is known as pico de gallo, a popular, all-purpose salsa.
       
10 December 1950, New York (NY) Herald Tribune, sec. 10, pg. 17, cols. 3-4:
Mexico Celebrates Christmas Early and Long, Dec. 16 to Jan. 6
‘Posada’ and ‘Nacimiento’ Are Traditional Features; Turkey Is Reminiscent of the Month
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A supper is served, at which there may be the famous Mexican Christmas salad, called “pico de gallo” or “cock’s beak,” which is made of beets, peanuts, water chestnuts, lettuce and other ingredients and dressed with a spicy sauce, buneolos, or crisp fried cakes, mantecadas (butter cakes), enchiladas, cold meats, preserved fruits, and, of course, the wonderful Mexican chocolate, foaming and tasting of spice and vanilla.
 
3 August 1954, Laredo (TX) Times, “The Mexican Parade: Pulque Furnishes Plenty of Vitamins” by Virginia Snow, pg. 2, col. 1:
“Pico de gallo” (rooster’s beak) is the name of another pulque. You buy the Mexicano kind and chop green chiles and plenty of onions and coriander in it.
 
23 February 1958, Independent Star-News (Pasadena, CA), Scene section (story about Guadalajara, Mexico), pg. 29:
Ponder this near-fatal event and its historical repercussions over a tequila chased by a “pico de gallo”  (orange, jicama fruit and small, red and hot chile pepper) and the stern stuff of the Mexican Revolution will seem real.
 
7 October 1962, Los Angeles (CA) Times, “My Best Recipe: Salad Relish Cools Off Fiery Latin” by Mrs. Robert Mercado, sec. E, pg. 17, col. 1:
PICO DE GALLO
(Comb of the Rooster)
2 medium-size tomatoes
1 large avocado
1 medium-sized cucumber, pared
1 teaspoon garlic salt
2 tablespoons olive oil
1 1/2 to 2 tablespoons lemon juice
 
Dice tomatoes, avocado and cucumber; toss together lightly and refrigerate until just before serving.
 
At table add garlic salt, oil and lemon juice. Mix carefully to avoid mashing. Serves 6.
 
12 April 1968, Latin Times (East Chicago, IN), “The Kitchen,” pg. 5, col. 1:
PICO DE GALLO
6 oranges without seeds
3 rutabogas (yellow turnips) medium
salt to your taste
chile to your taste
Peel oranges and cut into cubes. You do the same to the turnips. You mix them both and sprinkle with salt. You sprinkle some of the chile over it and serve the rest of the chile separately. Refrigerate and serve cold. Bien provecho!!!