"In Just a Heartbeat" was the second single from Burnette's self-titled 1980 LP (in true Peter Gabriel style, it was his third eponymous album). Neither the single nor the album charted, and I don't believe that the video received much in the way of airplay, as MTV wasn't launched until the following year.
Burnette would go on to have some success in country music, before joining Fleetwood Mac as Lindsey Buckingham's replacement in 1987. He left the band in 1991 (although he has sporadically worked with them since then) and returned to his country and rockabilly roots.
Cool trivia fact: Billy Burnette is the cousin of Rocky Burnette (below; the January 23, 2012 post). Rocky is the son of Johnny while Billy is the son of Dorsey.