Wall of Voodoo was a new wave band from LA., and originally formed in the late 1970's as a soundtrack company. The band's new wave approach, laid back vocals (almost talk-singing) and unusual music has led some to compare them to Devo, which is not totally unfair. I.R.S. Records (now who remembers them?) signed the band in 1980, and Wall of Voodoo's first EP had a cover of Johnny Cash's "Ring of Fire" that generated some buzz. While the band had some Western influences, their music is a bit tough to categorize; overall they were darker and more complex than one would expect from this song.
At any rate, "Mexican Radio" was the lead single from the band's second LP, Call of the Wild. The concept for the song came from the Mexican radio stations that the band used to listen to on AM radio in their car. In fact, the Spanish segments of the song were recorded from these stations. Similarly, the video was shot on the cheap, in Tijuana (in retrospect, I think that this helped the video). Overall, the video does a great job of capturing the eccentric song -- and I have to point out the "face in beans" scene (around 3:33) that was an iconic early MTV image.
Unfortunately, frontman Stan Ridgway left Wall of Voodoo in 1983, right after their appearance at the US Festival. The band continued for a couple of years before calling it quits. While Ridgeway did not have much success as a solo artist, he carved out a successful career scoring films.