Bassi and McShane apparently met in Ireland in 1984, where McShane worked as an EMT. The two quickly formed a band, with McShane as the frontman, due to his flamboyant style. There seems to be some dispute over who actually sung the lead vocals on Tarzan Boy, with several sources claiming that Bassi did the honors.
At any rate, the song became a huge success, hitting #13 in the U.S. (although it did even better in most of Europe). Unfortunately, the other songs from the Living in the Background album did not do as well, and a second album (1987's Survivor in Love) did not chart at all. Baltimora disbanded soon afterwards, and neither Bassi nor McShane had much success with their future musical projects. McShane died of AIDS in 1995. He was 37.
Cool trivia fact: A remix of Tarzan Boy charted, and nearly broke the top 40 in 1993 (it peaked at #51), after the song was used in a Cool Mint Listerine commercial. Here is your special bonus, from your friends at ERV: