I enjoy the way he clamps it into a timing machine, where it lies face-down against a microphone that amplifies its heartbeat - the ticking is the sound of the balance hitting the fork of the pallet - and generates a supremely analogue readout by way of a pencil-line on a strip of paper. How far off-centre that line wanders shows how much time the watch is gaining or losing.
I took to visiting Barber with such regularity that he finally asked me whether I wouldn't be happier with a battery-powered quartz watch. His implication was plain: my expectations of diamond-cut precision were unreasonable.
"The mentality of people today," he told me later, "is that they want a watch to be accurate to the second. But what's five minutes? If you can't wait five minutes, there's something seriously wrong with your lifestyle."
There are about three dozen moving parts in my watch: the force from the tensioned mainspring is transmitted to a weighted wheel which oscillates back and forth and, through a device called an escapement, moves small cogs which advance wheels, which advance more wheels. It's a miracle of micro-machinery not least because the essential technology is unchanged since the 17th century. But the interdependence of all those bits leaves room for error. Variations in temperature, in particular sudden ones, will affect the watch's accuracy. Leaving it by the clock radio will magnetise it into madness.
A watchmaker for 43 years, Barber says he got into the business because "my mother told me I was going to".
"I used to make a lot of models when I was a kid - tanks, planes, boats, that sort of thing. And when it came time to leave school, she said 'Well, watchmaking's all fiddly bits, and you enjoy fiddly bits', so I went along and got an apprenticeship at Len Greenlee's in Avondale."
In those days, every suburb had a watchmaker; the quartz movement and the throwaway Swatch put an end to that. But there's still plenty of work. Barber spent some time as a shift worker when his kids were young, - it suited family life better - "but it gave me more time to do watchmaking too. I always did it."
Unsurprisingly for such an artisan, Barber is disparaging about the quality of modern merchandise. I tell him about the Seiko automatic my father bought me for my 21st ("That would have been a 7005 calibre," he says without hesitation). It cost $95 - about three weeks' worth of my pay at the time. Now you can get a watch for an hour's wages.
"Hmmm," he says, "but the quality is not there. Quality is something that has disappeared, long gone."
He mentions a famous brand: "When you bought one of their watches when you were a young man, you bought a timepiece that would serve you for the rest of your life. Now if you buy one, you want to get rid of it as soon as you possibly can because it's garbage."
The workshop that Barber shares with two other watchmakers is a library of old watches in drawers and cases, from which they scrounge parts that are no longer made. There's a bench of lathes and drills where they make parts from new metal.
He loves the work, especially on old mechanical watches - he's just finished servicing an 1885 chain-driven model - because "there's no such thing as a straightforward job. Every job is a new challenge. And I like seeing how somebody sat down and thought about how to make this work. It's beautiful."