OK, so on closer inspection, it wasn't him after all. In fact, it was just Ian Astbury, auditioning for the role of singer in the re-formed Doors. Which, in fact, he would successfully land about 15 years later.
So the video is a lip-synching performance piece with this weird long-haired British American Indian wannabe, a peroxide Billy Idol clone on guitar, some sort of neo-psychedelic dood bass player, and the drummer for Big Country sitting in, apparently just collecting a paycheck (watch him just about bolt off the drum riser as the last notes ring in the air).
In 1985, when this was released, "alternative" acts just didn't do the things these guys do on stage in this video. First off, the long hair was a real no-no. The scarf, vest, headband, pendant, frilly shirt and fringe jacket, all possibly purchased at Steven Tyler's yard sale, were very unfashionable. Then there's the Daltrey-esque twirling of the microphone stand, the David Lee Roth jump splits, and the Jagger strut, all a pretty far cry from Morrissey and the other hip acts of the day.
The song itself is really interesting. Like the video, it combines a lot of disparate rock subgenres that didn't ordinarily mix together comfortably at that time. There are psychedelic sounds, an anthemic guitar part that fit in with the U2 and Big Country style of the day, and a hard rock attitude, all in a conventional "alternative" or "college radio" structure. This song, along with Love, from the same album, presented a kind of a watershed moment. It threw down the gauntlet and forced the hipster wannabes of 1985 (yeah, that was me) to decide whether there was more indie cred in admitting to liking it, or blowing it off as uncool and continuing to listen to Depeche Mode or something. It was a tough call.
A couple of years later, these guys blew up the playing field by growing their hair long and scraggly, putting on scruffy clothes, turning their amps up to eleven, and unapologetically turning into a full-fledged hard rock band. Guns 'n Roses opened for them! Their album, Electric, along with Nothing's Shocking by Jane's Addiction, and all the Led Zeppelin samples on Licensed To Ill, brought hard rock back to the punk kids who had grown up on it in the 1970s but rejected it after hearing The Clash (yeah, that was me).