Desvelado describes the state of being sleepless or having stayed up all night. It's a very expressive word that goes beyond simply being 'awake' (despierto).
In this classic song, the singer is desvelado because he's wandering the streets, obsessing over a woman's voice he heard on the radio. The word perfectly captures that feeling of lovesick restlessness and longing that is literally keeping him from sleeping.
Have you ever heard someone's voice and just fallen for them, without even knowing what they look like? That's exactly what happens in this song. Bobby Pulido sings about hearing a "voz de ternura" [voice of tenderness] on the radio and becoming completely obsessed. It's a wild idea, right? He admits he's in love with someone "que nunca la conocí" [that I never met]. His whole life now revolves around this search, listening to the radio every day just hoping to hear her again.
This isn't just a casual crush; it's keeping him up at night. The song's title, "Desvelado," means sleepless, and he is definitely not getting any rest. He wanders the streets, singing, "Voy desvelado / Por estas calles esperando encontrar / A esa voz de ángel que quiero amar" [I'm sleepless / through these streets hoping to find / that angel's voice that I want to love]. He's so determined that he vows to keep searching for her, even if it means he has to stay "desvelado y sin amor" [sleepless and without love].