Documentary film maker Seán Ó Cualáín, who is working on a follow-up after identifying up to five of the 11 men in "Men At Lunch," told The Local that the workers in question are "the two unknowns".
"Both of them have a question mark on them, most others have a claim," he said.
Ó Cualáín said there are five times more claims on positive identifications than there are men on the beam, but that the mystery is part of the image's appeal.
"There's a discrepancy but that doesn't lessen the power of the image, in some ways it makes it stronger because of it."
Historians have so far struggled to identify the men because there either was no official pay roll when the skyscraper at Rockefeller Plaza in midtown Manhattan was built in the 1930s, or it has been lost.
It was a perilous time for many workers, Ó Cualáín noted.
"There was one dead worker for every ten storeys. This was during the Depression, so there was a queue of people below waiting. If anyone was injured, and they often were, they'd be quickly replaced."
The image, with the eleven men without harnesses high above the rooftops of Manhattan, illustrates the risks workers took at the time. Ó Cualáín thinks the extremely tough times contribute to the picture's allure.
"Its a source of pride for everyone who claims their father is on that beam. It’s a story of eleven working men trying to put food on the table for their families during the Depression."
Although he and his team have so far identified only four or five of the men, he said many of the families who claim a link to the image do not care if they find proof or not.
"For most people who have a claim, it’s a family story that they heard when they were kids. It's a feel good picture, that’s why they’re happy to be associated with it."
Ó Cualáín and his team also got hold of a second image, which is taken slightly after the one that has made its way across the world on posters and other paraphernalia.
They know it is taken a few seconds later because the man on the far left who is lighting his cigarette in the original picture is puffing on it in the second picture.
This second image could be of interest to the Swedish family because it shows more of the face of the man seated fifth from the left. The Swedes think it is local man Albin Svensson.
Regional newspaper Hallands-Posten, which broke the story on Monday, noted that Svensson was slightly cross-eyed, although a family picture shows the condition was not severe, meaning it could be hard to detect even in the second picture.
The poster hangs in Ó Cualáín's production office.
"You can see slightly more of his face,” Ó Cualáín told The Local. "But you can't tell really if he's cross-eyed."