Quo's other frontman, Francis Rossi, remains equally game, but unlike Parfitt, he had to "neck a load of sick pills" before being filmed warbling in one of the biplanes' cockpits.
Rossi and Parfitt have appeared on Top Of The Pops more than 100 times, and have spent 23 years away from home while on tour. Some extra trivia for the Mastermind bod who recently chose Quo as his specialist subject: the band's road crew calls Rossi "Gomor", an acronym for "grand old man of rock".
In this, Quo's 40th anniversary year, they seem to be speeding up, not slowing down. Another mammoth British tour kicks off in late October, while, in a move that sees two great British institutions colliding, Rossi and Parfitt are currently playing themselves on Coronation Street.
Tonight's Quo show is the second of two at Carnival City, a vast casino-cum-concert-hall in Johannesburg, South Africa. Unsurprisingly, none of the inhabitants of the shanty town two kilometres away make it. South Africa is an untested territory for Quo, but their no-nonsense chugging functions as a lingua franca. You have to wonder, though, what the group's Eastern-looking PA, Lyane, makes of "The Oriental", a decidedly non-PC song.
The moment the gig is over, we get a police escort to the airport. If Quo are to make the filming of Top Of The Pops the following morning, it's imperative that they make the last flight out of Jo'burg. We reach the airport to find that it has been delayed. Nursing a vodka-tonic in the departure lounge, Parfitt drily delivers the first of many gags: "Somebody said to me yesterday, 'Lee Anne Rimes.' I said, 'No it doesn't.'"
Asked about his most memorable Top Of The Pops, Parfitt recalls a time when he and Francis were miffed at the absence of power outlets in their dressing room. Spotting a loose ceiling tile, they secreted some chicken madras near a heating pipe and left it to fester. "That was back in the Seventies," he says, laughing. "Perhaps it's still there."
Rossi homes in on the December, 1983, TOTP where Quo played "Marguerita Time", a double pleasure for him, as he wrote the song, and fellow guests Frankie Goes To Hollywood accurately predicted that it would claim the No 1 slot.
Back then, margueritas and cocaine were a nightly combo for Rossi. He once recalled seeing part of his septum disappear down the plughole while he was showering, but now his only addiction is keeping fit. "In January, when we're off the road, I go to the gym five days a week. When we're touring and I can't get there I get wound up; I feel like I'm letting myself down."
A ball of nervous energy, Rossi does seem a more complex, less happy-go-lucky character than Parfitt. "Our main focus tonight was to get to the airport," he says, "and for me that ruined the show. On the last British tour we had a run of six or seven gigs that I thought were horrendous. Luckily, it's like women and the pain of childbirth - you forget how hard it was."
Later, when I ask Rossi how he came to renew his song-writing partnership with Quo's former tour manager Bob Young - the pair had penned such Quo classics as "Caroline" and "Down Down", and are reunited on The Party Ain't Over Yet - he is more revealing. "I've been a heavy Catholic all my life, and one day this homoeopathic woman who treats me banged a copy of Conversations With God by Neale Donald Walsch down on my coffee table. I thought it was fantastic, and I realised that whatever bitter disagreements there had been between Bob and I were completely pointless.
"I phoned him, and we sat strumming acoustic guitars in my garden - lovely, it was. Now he comes round to eat, then goes home for another meal. My kids call him 'Bob Two-Dinners'."
At Heathrow, we transfer to Quo's tour bus. It has a double-bed-appointed area for Rossi which Parfitt jokingly calls "the sick room". Back at Carnival City, Parfitt and I had shot the breeze about Mick Jagger and Keith Richards's love/hate relationship. Echoes of Francis and himself, perhaps?
"The last person I want to see on a day off is Francis Rossi, believe me, but by the time we're back on stage, we're raring to go. We're not best buddies all the time, but it's not punch-ups either."
Having missed the rehearsal, the Quo arrive at the BBC's studios for what Rossi estimates is their 105th TOTP. He and Parfitt watch footage of their 1968 hit "Pictures Of Matchstick Men" then mime a rendition of "The Party Ain't Over Yet".
Indeed. We must immediately away for Quo to headline ITV's 50th anniversary celebrations. When the cameras roll, the band snap to it with a tight medley that takes in "Caroline" and "Rockin' All Over The World".
Later tonight, Status Quo will drive to Germany for yet more shows. Why do they do it? "Most of us in this business are insecure little show-offs," offers Rossi.
'The Party Ain't Over Yet' is out on SanctuaryReuse content