"Oh, go your regular pace," I reply, casual yet confident. "I'll keep up."
Let's just say that considerably more than three minutes elapse by the time a thoroughly winded columnist joins Heneghan at the top, where the views are as inspiring as the history.
The Absecon Lighthouse (abseconlighthouse.org) is the oldest extant building in Atlantic City. The tower soars skyward from the back of the keeper's house, which graces the rather forlorn corner of Rhode Island and Pacific Avenues with a glimpse of past glory.
The lighthouse went into service in January 1857. It still holds the 36-plate lens, custom-made in Paris and capable of beaming light from a kerosene flame nearly 20 nautical miles offshore to help ships navigate the dangerous waters.
"It's been here through everything, good and bad," says Heneghan, a married father of three who grew up on Long Island and lives in Ventnor. "The lighthouse is a great symbol of the city's strength and resilience."
The Absecon Lighthouse has survived at least 20 hurricanes and tropical storms, including Sandy. It has withstood "three earthquakes that I know of," says volunteer George "Buddy" Grover, 86, who wears a replica of a vintage light-keeper's uniform when he mans the tower on Fridays.
Decommissioned in 1933, the lighthouse has been owned since 1966 by the state, which completed a $3.4 million restoration project in 2003. About 28,139 people - more than twice the number of a decade ago - visited last year.
"It's up to us to keep the light shining," says executive director Jean Muchanic, whose nonprofit organization is responsible for an annual budget of about $225,000.
Income comes from tower admissions ($7 for adults), gift shop sales, weddings, other events, grants, and donations; the grounds, museum, and parking are open to the public at no charge.
"We focus on marketing," adds Muchanic, who is as personable, enthusiastic, and knowledgeable as every last one of the half-dozen employees and staff I chat with.
"And that's where Dan comes in."
Heneghan, the longtime public information officer of the state Casino Control Commission, notes that he's walked the Boardwalk several times a week for years.
But after attending a birthday celebration for the lighthouse in January 2013 ("I came for a piece of cake"), Heneghan realized that a climb offered a good alternative to walking in bad weather.
He became a lighthouse member, so he can climb for free, and this year decided to invite family and friends to kick in $1 each time he does so. About 10 have agreed to participate so far.
"My goal was to make 50 climbs this year. It's a great motivator," Heneghan says. "I don't have a dollar goal. I just want to get people involved, and interested."
He's onto something. After all, until I heard about his climbing campaign, I'd never set foot in the place. Much less seen the view from the top.