The relationship began when Stoops was named defensive backs coach in 1997 at Wyoming. Eliot, then a junior linebacker, immediately noticed him.
"I was a player at Wyoming when Coach Stoops was a coach there and he's this young, fiery 20-something-year-old coach," Eliot said. "He was really confident and I (thought), 'He's almost too confident for his age.' "
It turned out Stoops' confidence wasn't unfounded. He took a secondary that had previously ranked among the nation's worst and shaped it into a unit that intercepted a school-record 24 passes in his first season.
Eliot, meanwhile, was forced by injury to give up playing football before his senior season. So while he completed his undergraduate studies, he got his coaching start as a student assistant, working alongside Stoops every day. They didn't know it at the time, but Stoops and Eliot were forming the foundation of a partnership that would reunite them at Houston, Miami and Florida State, duplicating the defensive success they had at Wyoming from 1997-99 everywhere they went.
Having spent eight seasons with him, it was only natural that Eliot would follow Stoops when he was named head coach at Kentucky. But for a brief moment, it looked as if the two might be separated.
"I thought Coach Eliot and I had a plan as we were going through this process," Stoops said. "I thought he was in the boat and then he started getting all these opportunities. That's what you want. You want coaches that have a lot of value, that have a lot of opportunities."
Ultimately, Eliot signed on as defensive coordinator, filling a role that would be vital as Stoops undertook the balancing act that is being a head coach for the first time.
"Coach Eliot and I have been to three, four, five stops together and he knows what I want to do defensively," Stoops said. "So that was very important to let me do all the things that I've been doing in the community, get out there and be in charge of the whole program."
On Friday, Eliot joined Stoops on stage at the Kentucky Football Kickoff Luncheon as he fulfilled the final of his face-of-the-program responsibilities before the Wildcats report on Sunday for fall camp. A sellout crowd of 450 was in attendance at the Patterson Ballroom of the Lexington Hyatt Regency, listening intently as Stoops, Eliot, offensive coordinator Neal Brown and special teams coordinator and safeties coach Bradley Dale Peveto previewed the 2013 season.
Stoops interacted with all three as if he had known them as long as he has known Eliot, but the familiarity he has with each is actually quite varied.
Peveto, then a cornerbacks coach, was with Stoops and Eliot at Houston in 2000, but that's the extent of their relationship prior to their arrival in Lexington.
"He and I worked together at Houston for one short year, but he made an impression on me," Stoops said. "He makes an impression on everybody that he works with."
That - and his vast experience over 26 years as a college coach, one of which was spent winning a national title at LSU in 2007 - was enough for Stoops to reach out to Peveto when he was searching for a special teams coordinator. It didn't take long for Peveto to become interested.
"The thing that excited me the first conversation I had with Coach Stoops was that he's committed to special teams," Peveto said. "If you don't have that commitment from your head football coach, it's hard to succeed and be very good at it."
Peveto delivered his remarks in his characteristic Texas drawl, an accent Stoops has clearly come to enjoy.
"That was in New York, right?" Stoops joked when Peveto recalled his youth as the son of a football coach. "Did you grow up in New York? Where's that accent from?"
As for Brown, Stoops knew even less before hiring one of the game's bright young coaches. As he began the process of seeking out an offensive coordinator, Stoops kept an open mind.
"I had some other ideas in mind as Mitch and I were talking and I was very honest with (Athletics Director) Mitch (Barnhart) when I said, 'Nothing's set in stone. I understand that is one of the most important hires I can make because of my background on defense,' " Stoops said.
It was fortunate Stoops was willing to listen, because Brown wasn't even on his radar initially.
"After I was offered the job, somebody brought to my attention that Neal could be interested and he was from Kentucky and I didn't even know all that," Stoops said. "So I started looking at Neal on paper and looking at all the things he did."
Brown has coached some of the best offenses in the country at Texas Tech and Troy and has deep Kentucky ties as a player and native of the Bluegrass, so he looked good enough at first glance for Stoops to place a phone call. When he did, Brown was driving with his wife and two daughters from Lubbock, Texas, to Dallas. Accustomed to life with young children, Stoops was unsurprised to hear crying in the background.
"He's like, 'Coach, you know, maybe I could just call you when I get there,' " Stoops said. "I said, 'I have a couple young kids. If it's alright with you, it's alright with me.' We just kept that conversation going and I was very impressed with him on day one."
The rest of the coaching staff was in the crowd for the Kickoff Luncheon, serving as more proof that Stoops found the best possible coaches regardless of how well he knew each one beforehand. At one table was tight ends coach Vince Marrow, who has an even longer history with Stoops that Eliot after growing up with him in Youngstown, Ohio.
"I had to bring my homeboy in here, right?" Stoops said.
Seated nearby was Jimmy Brumbaugh, with whom Stoops had coached at a camp.
"He coaches defensive line exactly like we want it to be taught," Stoops said.
Tommy Mainord, meanwhile, has worked with Brown, but never Stoops.
"His wide receivers were as tough as anybody in the country at Texas Tech," Stoops said.
But as different as each member of the coaching staff's background may be, they have the most important things in common.
"They're unbelievable workers," Stoops said. "Those guys just bring such great value."