"When he goes into a build-up phase, he does three training sessions a day," says dad Walter. "Some of them are in the middle of the night. The house shakes and the dog runs outside. We might be asleep, and he'll be lifting weights or bounding up and down the stairs to our bedroom door. He's definitely different. How we ever produced that, I'll never know, but we're very proud of him."
Of course, part of Jacko's success can be traced back to his parents. Walter was twice national shot champion back in the late-1980s, while mum Nerida won a discus title. They deliberately steered their son away from rugby and encouraged his sporting passion through football and basketball before unleashing him on athletics. Older sister Ayla has an American college scholarship at South Methodist University in Texas as a hammer thrower.
"I was born with sporting talent, but no more than a lot of other boys," Jacko says. "After talent, work ethic and focus is everything. My desire to achieve my goals is unbending, to the point where, even as a 10-year-old, I would throw in the dark at 11pm rather than miss a session."
At 1.9m tall and weighing just over 100kg, Gill isn't huge by shot standards, but successfully combines speed and athleticism with his increasing strength. Perhaps the biggest difference between him and his rivals is between the ears.
"Aiming for that big throw is about more than just physical preparation, so the size and age of my competitors never phases me. Mental preparation is where it's at and mine starts some two weeks out as the event nears. "It's as much about intensive visualisation and getting extra out of your body. I believe most people have this, but just don't know how to use it. Many times, my warm-up before a big meet is to lay down on the track and plan how I will win it, while the other throwers are busy throwing. The three days before are very important and I don't talk much as the tension builds."
You can imagine the air of anticipation in the Gill household over the coming weeks. All three targets are formidable, and will require subtle adjustments in technique and timing.
"All of the three have been dreams and the task won't be easy," he says. "But the Olympics have been my goal since I was 10, so I suppose that's the most important to me. If I qualify early, I can then build up over a longer period for the Olympics.
"Throwing the 5kg over 25 metres is a target that wasn't thought achievable, but it's one of many boundaries I hope to break. About a year back, I threw the 4kg shot 26.67m in training, so the distance is not new to me - it's just another step in my development."
In the long term, though, beating Storl's mark might hold the most intrigue. The young German, still only 21, surprised everyone by beating his more experienced rivals at this year's world championships in Korea. Many predict he'll dominate the event for the next decade, but that kind of challenge clearly inspires Gill. Their rivalry could become one for the ages, starting in London next year.
"To be honest, I can't wait to compete against him," he says. "The Germans have been dominant shot putters over many years, but I feel Valerie Adams and I could bring that domination to the South Pacific."
The one fear among all this is that such precocious talent in one so young might burn out before it realises its potential. It wouldn't be the first time.
"Long-term - not too long-term - I want to win gold at the Olympics," he explains. "What I've achieved so far is simply what's required if one is to achieve at senior level. If you're not winning world youth or junior titles and breaking records, then you won't be winning at high level as a senior.
"For me, now I must add strength to my body, while maintaining speed. One day, when I tire of shot, I may have a serious go at discus, where the training is not so intensive." Gill also holds the NZ U18 discus record at 62.05m.
Away from the track, he doesn't waste too much time on traditional teenage pursuits, preferring to focus on training. But he has an impressive collection of friends including the current shot world recordholder American Randy Barnes.
"He's invited me over to stay, but trying to find time to do this is hard. Many fellow athletes have stayed in touch with me and it's always a thrill to hear from them."
He also collects lizards - Blue Tongues and Bearded Dragons from Australia, to be precise. "These are amazing pets and something I really enjoy."
Walter chuckles: "People who win things aren't going to be like your average person. Champions are different."