Neilson's notoriety in the rest of Philadelphia is likely to get a boost on May 20, when he will be the Democratic candidate for an at-large vacancy on City Council.
He is facing Republican lawyer Matt Wolfe and Libertarian Nikki Allen Poe, a marijuana legalization activist, but with Democrats holding more than a 6-1 edge over the GOP in voter registration, Neilson is the heavy favorite.
The winner will likely take a seat on Council in time to vote on the biggest issues facing the city this spring - the budget, the school funding crisis, and the proposed sale of the Philadelphia Gas Works.
As an at-large Council member, Neilson, 50, would be representing the entire city for the first time.
"What's good for the city as a whole may not be what's best for my neighborhood all the time," he said. "I can handle that."
Since the rules of special elections allow parties to hand-pick their candidates, Neilson's selection by Democratic ward leaders in March amounted to a virtual coronation.
Not that he's taking anything for granted - he's particularly worried about a kind of ballot confusion that has sunk candidates before.
"There's another guy named Wolf who spent $10 million in commercials," he said, referring to Democratic gubernatorial candidate Tom Wolf. "I think about it every day. It's hard to sleep."
If Neilson wins, the question becomes whether he can position himself for reelection next year, in the normal cycle, in what could be a highly competitive field of at-large Council candidates seeking four-year terms.
The special election was called after Councilman Bill Green left to become chairman of the School Reform Commission.
The last time Council members were seated in a special election, in 2006, two of the three were tossed out of office in the next election.
"I'm not just going to make a cameo and shake hands," Neilson said. "When the people of Philadelphia see how dedicated I am to them, I think I'll have a good shot in a competitive field."
He said hard work has been a hallmark of his career, something he learned in a family that treasures blue-collar values.
His grandfather joined Local 98 in 1923. His father, brother, and one of his five sons are electricians. He said his grandfather's union pension "saved him" when he was living on a fixed income at the end of his life.
"You want to be able to allow people to retire with dignity. Don't take that away," he said. "Because, at the end of the day, if they can't, they're going to be a burden to society at the end."
When Neilson graduated from Abraham Lincoln High School and joined the union, Local 98's employment and influence were at a low ebb.
At first he went the journeyman route. It took him to Denver, where he worked for months on the new airport. Then Dougherty, Neilson, and a group of young guys made a power play at the union.
"We pushed and pushed and pushed," Neilson said. "We had to make sure our future and the future for everyone around us was secure."
Local 98 has since grown into a powerhouse, its influence felt throughout the city in development, policy, and politics.
Neilson was an integral part of that ascension, working on political campaigns, including Rendell's gubernatorial races. He also ran the campaign that put Local 98 member Rick Mariano on Council. Mariano later served four years in prison on federal corruption charges.
Dougherty said of Neilson, "Eddie's job back then was to create what has become the Local 98 political machine."
Neilson hasn't been formally involved with union, however, for a decade.
Rendell tapped him to be a deputy secretary of labor and Neilson also worked in the state Department of General Services. He lived in a small rented room in Harrisburg, sleeping on an air mattress and driving home to his family on the weekends.
Neilson also won his seat in the state House in a special election, when Dennis O'Brien, the longtime Republican representative, left to join Council.
Neilson said he had a bipartisan voting record in Harrisburg and he's always worked well with the GOP - O'Brien, he said, encouraged him to run for his old seat.
Because of redistricting, though, Neilson was pitted against another incumbent, State Rep. John Sabatina Jr., in the Democratic primary. Party leaders were not shy about saying they wanted to avoid that nasty fight.
But Neilson said his polling showed him ahead in the race against Sabatina.
"I didn't walk away from something because I wasn't winning it," he said. "I left the House seat, chose to take this on, because seven out of 10 issues that come through my office are city issues."
Neilson intends to stay on Council, relying on something he said he learned in the trades:
"If you don't work hard, you're the first one to get laid off," he said. "I don't want to be laid off from City Council before I start."