Two books have also been published under the inscrutable1
title of Suicide Blonde
The first is Suicide Blonde: The Life of Gloria Grahame, a biography by Vincent Curcio of 1940s/1950s semi-star and Academy Award winner Gloria Grahame. The INXS song written up above was released in September 1990 as the first track of the album X. Curcio's book was published by William Morrow & Co in October 1989, predating the song by some 11 months, so it stands to reason that Hutchence & Co borrowed their title from it. Meanwhile the book itself was never reprinted, and copies of the first edition go for between $100 and $500 in used bookstores. Although Grahame was not nicknamed Suicide Blonde during her lifetime, after the publication of the book the name stuck and she is known as such on several websites.
Suicide Blonde by Darcey Steinke was published by The Atlantic Monthly Press in September 1992. It is a supposedly trendy-erotic "tale of kinky sex and all-out depravity" (Kirkus Reviews). The least critically successful of Steinke's novels, it nevertheless became a cult item and has been translated in seven languages.
1 Not as inscrutable as I thought. Naturally, she dyed by her own hand (quote attributed to Saul Bellow). Thanks to Pseudo_Intellectual.