At times, candidates flashed revealing glimpses of their interior lives. When we asked, for instance, where they would travel on their first foreign trip as president, it was immediately apparent which Democrats had spent time envisioning that trip in their heads. Former Representative Beto O’Rourke of Texas instantly named Mexico, while Senator Cory Booker of New Jersey replied with unmistakable sincerity, “I’ve given a lot of thought to that, and it’s not something I’m going to be telling The New York Times about right now.”

[See their responses on where they would go on their first international trip as president.]

But some of the most telling — and in some cases, jarring or endearing — moments with the candidates happened off camera, or outside the context of the interview. Mr. Hickenlooper, for instance, showed up at our office flustered because he had lost his wallet, and confessed sheepishly that it had been a long time since he had dealt with certain indignities of being a private citizen. Learning after the interview that his flight home had been canceled, Mr. Hickenlooper took the development in stride; he lingered in the newsroom, bantering with our colleague Stephanie Saul about Teddy Roosevelt’s relationship with the muckraking reporters of his day.

Ms. Harris arrived at the newspaper with a complaint and a request. She asked Patrick Healy, our politics editor, if The New York Times could make it easier to read articles offline on the paper’s smartphone app — an important consideration for a West Coast lawmaker who is regularly confined to transcontinental flights with spotty Wi-Fi.

Ms. Harris — who was at her most animated in the interview when discussing her passion for cooking — also asked to meet Sam Sifton, the food editor. Soon, the two were kibitzing about recipes amid a maze of desks and a gathering crowd of onlookers. (Ms. Harris was less excited when Carolyn Ryan, a masthead editor, approached to ask her about a blossoming late-March crisis for Mr. Biden, involving his physical behavior with women.)

Mr. O’Rourke, similarly, was animated befor e his interview : On a sound stage in Austin, Tex., where we met him, Mr. O’Rourke spent more than a few minutes chatting with our photographer, Tony Cenicola, about their erstwhile rock bands. And Mr. Booker tolerated some joshing about his high-profile personal life — he is dating the actress Rosario Dawson — before pleading that the exchange be treated as off the record.

Some candidates were attentive to their self-care routines in the chaos of a campaign. Gov. Steve Bullock of Montana, who visited the office during the tumult of his campaign kickoff, left in haste after his interview — so that he could take a run in the city before hopping on a flight to Iowa.

And a few were plainly reluctant to meet with The Times .

Mr. Sanders, who periodically castigates the news media, resisted scheduling an interview for months, and told a reporter jokingly in mid-May that he would consider participating in the video project to reward the newspaper for its “wonderful treatment” of him.