Alas, Bruce says he has no memory of the song or how it ended up in the film.

My guess, then, would be that it came from someone other than the screenwriter. Can’t ask Douglas Trumbull, the director, he died a few years ago. (I didn’t think to ask him this question when I spoke to him at a Q&A session several years ago when he was still alive.) Natalie Wood famously died during the film’s production. I suppose I could see if Christopher Walken remembers? Wonder if I could contact him through his agent or something. It seems unlikely that he’d know or remember, so I probably shouldn’t bug him.