In interviews, Esquivel's family members have stated that the young boy started playing piano when he was around 6 years old, to the amazement of older musicians who would gather around him in disbelief and to his own delight exhibiting his musical gifts.

He used many jazz-like elements; however, other than his piano solos, there is no improvisation, and the works are meticulously arranged by Esquivel himself, who considered himself a perfectionist as a composer, performer, and recording artist.

A survey of Esquivel's recordings reveals a fondness for glissando,[3] sometimes on a half-valved trumpet, sometimes on a kettle drum, but most frequently on pitched percussion instruments and steel guitars.

That album's song "Mucha Muchacha" makes unusual use of stereo separation, with the chorus and brass rapidly alternating in the left and right audio channels.

He arranged many traditional Mexican songs like "Bésame Mucho", "La Bamba", "El Manisero" (Cuban/Mexican) and "La Bikina"; covered Brazilian songs like "Aquarela do Brasil" (also known simply as "Brazil") by Ary Barroso, "Surfboard" and "Agua de Beber" by Tom Jobim, and composed spicy lounge-like novelties such as "Mini Skirt", "Yeyo", "Latin-esque", "Mucha Muchacha" and "Whatchamacallit".

The album's concept was that Esquivel's music would be combined with sound effects and edited in a way that suggested a visual work such as a film, though without dialog or an explicitly stated narrative.

[6] His recording of his composition "Mucha Muchacha" was used in the films Confessions of a Dangerous Mind,[7] The Big Lebowski,[8] The Notorious Bettie Page, Stuart Saves His Family, Nacho Libre and Beavis and Butt-Head Do America.