Even among the multi-hued extravagance of the decade, Bailey and his fellow Twins Alannah Currie and Joe Leeway stood out. Their clothes were brighter, their hair higher and their multicultural, male/female line-up, theatrical approach and embrace of the synthesiser set them apart from their New Wave peers.
"We weren't the standard group of teenage friends, we were a complicated group of people," Bailey says from Virginia, America, where he's currently touring with Boy George and the B-52s. "That we happened to be two men and a woman, and a black person and two white people, meant there was always a very interesting frisson of where we were coming from culturally. The mix didn't all come from the same neighbourhood."
So what, after all this time, has brought him back to pop music?
"About three years ago I started performing some of the old hits and enjoying it. I felt, 'this is good but I don't want it to just be nostalgia. There has to be some current creative engagement'."
This saw him dusting off the old pop playbook.
"People tend to see pop as the cute and meaningless cousin of rock 'n' roll. A three-minute pop song has to get everyone singing along, tapping their feet, and mean something. That's incredibly difficult. There's a lot that has to be compressed into a very short space of time. There are skills involved that I hadn't engaged with for a long, long time. When I did, I got the feeling of bumping into an old friend."
He says pop music was something he had been consciously avoiding. But why?
"I needed to escape from it," he replies. "So many things had been put aside because the Thompson Twins were so demanding of time and energy. Basically, I retired from pop music."
He says his world changed, along with the Thompson Twins' fortunes, when he finally saved enough cash to buy his first synth.
"What I didn't realise was that it liberated me. As a songwriter, as a music composer and from having to do the same lineup of a band all the time. With a synthesiser and a drum machine you can say we're no longer instrumentalists. What we are is the designers of a pop experience," he says. "That sounds pretentious but it was actually a revolutionary moment for us. It was so powerful. The idea that we didn't have to fit in a role for everyone. We were no longer tied to the line-up of a band. It was incredibly liberating. I think that was the major step forward for our success."
He's on tour overseas until November. Hopeful, I ask if he'll play a show here?
"I wish," he answers, making two of us. "It's incredibly expensive for us. I was made a very, very nice offer by a New Zealand promoter but we just couldn't work out the finances. But also, there's a part of me that treats Auckland like it's my village, you know?"
Then he laughs and says, "I want to sit on Ponsonby Rd drinking coffee. I don't want to be signing autographs."