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Campylorhynchus brunneicapillus
About 14 cm (5.5 inches), very distinctive call. "A conspicuous sight and sound of the Southwestern deserts, the Cactus Wren is the largest wren in North America. Although it can be found in urban backyards, it is a true bird of the desert and can survive without freestanding water."
Rocky semi desert with little vegetation and water.
Thank you bee.jacbs for the ID. It is a Cactus Wren, the call is the same as the one from the page of Cornell Lab of Ornithology, once you hear it you know it is the one.
It looks a lot like a cactus wren, but I'm not familiar with all of the wren species in Mexico.