Now, the 34-year-old father of four wants to focus on how the youth are doing in his town and keep working at KIA/Polarnet as an Internet service provider.
Sam Tulugialik will be replacing Neeveecheak as he was elected mayor on Dec. 13.
"I thought I'd try it for a year. I could handle it, but I'm too young for that kind of stress," said Neeveecheak during a phone interview last week where he talked about his adventurous past and his future plans.
When Neeveecheak was growing up, he avoided the troubles that plague many Northerners, including alcohol and drug abuse, by getting heavily involved in sports.
He hunts, too. He also taught himself how to make an iglu after many, many failed attempts.
"I used to do a lot of working out. I even taught myself how to do a back flip," he said.
He broke a record in the one foot high kick at the Arctic Winter Games when he was 15.
After that, his love of sports was solidified.
That is what he hopes to pass on to his own four children and the youth in Taloyoak now that his mayoral duties aren't taking up all his energy.
He also wants to spend more time assisting people in various ways such as helping them get prospecting licences or getting money from Inuit organizations.
Neeveecheak feels compelled to help his people. He calls himself "lucky" despite a life punctured by pain and hardship.
He had a brother who drowned at a young age.
He didn't have many luxuries growing up in a "small little house" in Taloyoak. For warmth, he and his sisters would often huddle near the stove.
But his family was close and his mom told them old stories to capture their imaginations and help them fall asleep at night.
The old Inuit legends always had a moral to them, and the one that stands out for Neeveecheak the most is the story of Kiviok, the adventurous boy who travelled far and wide.
Kiviok begged a friend not to break the news to his parents that he was returning home, but the friend didn't listen. Kiviok's parents dropped dead on the spot from excitement and happiness when they heard the news.
"The moral of the story is listen when someone tells you something."
Now he passes on the stories to his kids who are getting old enough (the oldest is 13) to appreciate their lessons.
Neeveecheak hopes the youth in Taloyoak will also appreciate his work with them now that he has more time.
He also hopes a trailer recently donated by Lyall Construction to the town will become a youth centre.
His role will be securing funding so that youth have plenty of opportunities to improve their lives.