Ok folks, I used Shazam (again) on the clips Dave Stewart posted to his Facebook. I was able to tag that unknown clip, Shazam (the app) says it's actually titled "I Don't Care," and recognized that it was by Stevie Nicks. Edit/caveat: it also says "I Don't Care" is the name of the album, and there is always the possibility that someone burned the audio of that clip, with that title, to a CD and uploaded it to one of the CD databases - while possible, that seems somewhat unlikely.
That's not on any tracklist we've seen, and now we (maybe) have a title.
