To Idelson, that moment speaks volumes about the hold the Hall of Fame -- and Cooperstown -- has on its honorees. It's where they come to be young again, to catch up with their buddies and tell war stories.
"The idea is to have them feel this is their home away from home," Idelson said.
It's special every year when new Hall of Famers are inducted. For those like Niekro, there's an enduring magic that draws them back at various times through the year.
"It's a sacred place for me," Niekro said.
The former knuckleballer, winner of 318 games, inducted in 1997, loves the place, its setting, its beauty. So do others.
"For me, it's a small town, peaceful, serene," Andre Dawson, the former Expos and Cubs outfielder, said. "It seems like life kind of slows down there. You get to kick back and enjoy the scenery. I always look forward to getting back there."
Dawson also loves what the Hall of Fame represents. Being chosen to be in it is baseball's highest honor, and after all the hard work and all the dreams, returning to Cooperstown is a chance to be part of one of the most elite clubs on the planet.
Only 211 players have been inducted into the Hall of Fame, out of the 15,000 or so who have played Major League Baseball. There are 306 inductees in all, including managers, club executives, umpires, etc.
One of the greatest tributes to the people who run the Hall of Fame is that so many Hall of Famers return to Cooperstown each summer for induction weekend. This July, the Hall is expecting around 50 of the 67 living Hall of Famers to return when Greg Maddux, Tom Glavine, Frank Thomas, Tony La Russa, Bobby Cox and Joe Torre are inducted.
That weekend, Hall of Famers will welcome the newcomers and catch up with one another, tell stories and soak in the atmosphere.
"I call it a connection," Niekro said. "It's a connection to fans all over the country. It's a chance to shake hands and sign autographs. The people at the Hall of Fame -- [chairman] Jane Forbes Clark, Jeff -- they do such a great job. They make you feel like it's our town. You're sitting out there on the back veranda of the Otesaga [Hotel], and it's just beautiful. It just doesn't get any better."
Some of the Hall of Famers will be in Cooperstown on Thursday when the Hall of Fame celebrates its 75th birthday. Like induction weekend, all the right touches will be in place.
"Everything is done right," said Rollie Fingers, the former reliever who was a three-time World Series champion with the A's and was inducted in 1992. "We stay in the Otesaga, a beautiful hotel. They cart us around, take us to parties, have nice dinners."
Beyond those things, though, is the honor that all the hard work and all the commitment have gained them the highest possible honor.
"You're sitting there with the best to ever play the game," Fingers said. "I idolized some of those guys growing up."
It's a surreal experience for a baseball fan to look at that stage during the induction ceremony and see Willie Mays, Henry Aaron, Frank Robinson and so many of the other legends of the game.
"To see them in one place at one time and enjoying being here, I still get goosebumps," Idelson said. "For a baseball fan out in the audience, to not only see their favorite player get inducted, but to see the greats of the game welcome their favorite player into their fraternity, it's pretty moving, as it is to the players themselves."
Indeed, it's an amazing experience for everyone.
"My childhood idol was Sandy Koufax," Fingers said. "I grew up watching him from the fourth deck at Dodger Stadium. Now I'm sitting there having dinner with him, having a bottle of wine. That's one of the reasons I go back."
As Earl Weaver was about to give his induction speech in 1996, he was greeted by an ocean of Orioles fans applauding warmly and chanting his name.
For that one moment, Weaver must have been transported back to perhaps the best days of his life, when he managed Baltimore to four pennants and a World Series title.
"Don't make me cry," Weaver pleaded as the fans continued to shower him with love.
Hall of Famers run down a list of things they like about induction weekend, from seeing the guys again to feeling the love of the fans.
Some weekends in years past, there would be Ted Williams out on the back porch of the Otesaga holding court on hitting.
Or Stan Musial playing a few notes on his harmonica.
"Another attraction is the camaraderie of seeing fellow Hall of Famers," said Jim Palmer, Weaver's star pitcher who was inducted in 1990. "The war stories are priceless. Also, very important, is the way baseball fans, old and young, come to Cooperstown to continue their love affair with baseball.
"It doesn't matter what team you root for, they just love the game. The connection Roger Kahn talked about in 'The Boys of Summer,' of being able to compare one generation to another, is palpable. It is a great weekend and a great destination for baseball people."
Palmer fell so in love with the Cooperstown experience that he got married at a spot overlooking Lake Otsego in 2007.
"First of all, how special is it that you have gained entry to the Hall of Fame?" Palmer said. "You are treated royally by Jane Clark and Jeff. Cooperstown is very Norman Rockwell-ish. Upstate New York, Lake Otsego, is idyllic."
Fingers said his induction was a hectic time. Since then, though, he has attempted to soak in the entire experience.
"Now I like listening to the speeches, especially the guys I played against," Fingers said. "It's an honor to go there in the first place. I've gone back every year."