On the surface, rugby does not appear to be a natural fit for Dunne.
Tawa's under-21 side are hosting the Upper Hutt Rams at Redwood Park, just north of Wellington. The park is the kind of rugby ground you see in every town in New Zealand: an uneven, patchy field, a grass embankment for a grandstand, and a concrete-block changing room.
About 50 people are scattered around the pitch; a couple have pit bulls on leashes. One of the wingers slips away from the field for a quick cigarette before running back on for kick-off, discreetly puffing smoke out the side of his mouth.
"It's far more real than the hype that sometimes surrounds the very top level [of rugby]," Dunne says.
Standing on the embankment in a leather jacket, black scarf, black trousers and shiny shoes, he spells out his rugby credentials.
He is a long-time Crusaders fan because of his Christchurch upbringing. He has an All Black grandfather Frank Smyth, who has the unusual record of playing only five first-class matches, three of them for the All Blacks.
Dunne also played, taking a place in the back line while a student at St Bede's College, which has produced more politicians, chief executives and judges than any other school in the country.
"I've always been a far more active spectator than participant," he says.
Five minutes after kickoff, Dunne's local side Tawa are down 10-0.
In a huddle around the goalposts, their captain barks at his players: "What's happening?"
Dunne mutters: "What's happening? You're getting creamed."
Trudging back to the halfway line, the captain yells loudly: "This is bullshit, guys."
Dunne grimaces a little.
"I must say, when I was a player I always thought that [swearing] was over the top. It's great to win. But it's only a game."
We stand in silence for a while. I ask whether he is pigeon-holed because of his appearance - the bow-tie, the hair. Did he suggest a rugby game as a counter to the public perception of him as fusty or boring?
A little exasperated, he shoots back. "I am pigeon-holed. I have been for a very long time. I am the original Mr Boring and I have never worked out why.
"The fact that I wear a bow-tie makes me some sort of eccentric, which I would have thought negates the first point.
"The other thing I'm pigeon-holed for is that I have a fair head of hair. It is not quiffed. It is not coloured. It is not styled. It is entirely natural.
"My hairdresser said to me the other day 'Your hair is like a river. It changes its own course and goes its own way and there's not much we can do about it'."
He pauses for a moment.
"But I never ever try to let that stuff get to me. I just find it very amusing and if anyone took the time to get to know me better they'd know all of that stuff was nonsense."
Are some of his stunts - planking on a television show, taking selfies, pulling a duck-face - a bid to shake this "boring" image?
"Yes and no. I do it because that's the sort of thing I'd do anyway. I've got a reasonably zany sense of humour and I quite like the absurd from time to time. Those sorts of things aren't stunts. They are just part of me."
A few children on the embankment giggle as Dunne poses for photos with the Herald photographer.
On another occasion years ago, a funeral director asked him to have his photo taken in a casket as a promotional stunt.
"There was no suggestion of political malice involved. But in an election year, I'm not going to have a picture of me lying in a coffin."
Like the diverse electorate he lives in, Dunne moves between several worlds. The night before, he was at a Royal New Zealand Ballet performance.
"I made a couple of comments to people about how I was going to the ballet. And I was surprised that that was still reacted to as a bit odd.
"I thought we'd moved on from that. But I think it's still ingrained in New Zealanders, a sort of wariness of the arts, a sense that people who like those things might be a little bit putting on airs and graces, presenting themselves as superior."
He won't say what the reactions were. Later on, I check his Twitter feed. Dunne had written that he hoped his flight landed in time for the ballet.
"Just leave your man card at check-in," one tweeter replied.
On the field, the one-sided match continues with another Upper Hutt try. "No, no, no, no," Dunne winces.
Dunne's All Black grandfather had another legacy - a connection to the Labour Party. Smyth grew up in a boarding house on the West Coast which housed miners, many of them senior Labour Party figures who became close friends. He handed his political interest on to Dunne, who joined the party aged 17.
"Today, I'd be described as a nerd," he says, noting that he began ordering copies of parliamentary debates when he was 14. Did he ever want to be anything but a politician?
"I wanted to be a sea captain, I suppose. I always fancied myself in a uniform on the bridge of a flash ocean-liner."
After he left high school, student politics swallowed up his week-nights and Saturdays and put an end to his rugby.
Dunne is still a Catholic, but won't say whether he still prays or goes to church. He has a liberal voting record in his 30 years as an MP, and was an early supporter of decriminalisation of homosexuality and abortion law reform.
He says he was never completely at home with Labour, which he felt impinged on his belief in free will and personal responsibility. He was also uncomfortable with party members parading their poverty.
"I've been to private schools. I wasn't brought up in a state house. I started to feel out of place in the sense that my values were out of place. At the time I represented the most wealthy electorate in the country."
A low, late sun is now casting long shadows across the pitch. While we were talking, Tawa has staged a dramatic comeback, nearly winning the match.
An elderly woman on the sideline waves at Dunne. Later, I ask her whether she's ever seen him at a rugby match.
"No, and I'm here most weeks. But he's always at school galas, at other stuff. He's done well for us, he got us Transmission Gully."
Dunne doesn't bother to press the flesh at the rugby game. Unusually for a politician, he hasn't spoken to anyone except the photographer and me for two hours. He says that he doesn't even bother putting his face on his billboards anymore.
"I don't need to go up people and and say 'Hello I'm so and so'. They all know who I am."
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