The players held up to each and every lad making his way through the youth system as shining examples of just what can be possible.
Their very names command a certain degree of reverence. Work hard, listen and learn and there will be a time when you can follow in the footsteps of the two Jameses, McCarthy and McArthur.
For some of those young men who have risen through the ranks at New Douglas Park and bought in to that mantra, the time is now.
Alex Neil, the player-manager, concedes this is the Lanarkshire club's big chance to break back into the top flight, with the first instalment of a two-legged play-off against a Hibernian side devoid of goals and belief just hours away.
Rangers and Hearts will be in the SPFL Championship next term. It will, without question, be a dogfight. This team has to seize the moment and capitalise on this momentous opportunity because the rewards, personal rather than collective, could be astronomical.
Neil played with McCarthy and McArthur at Hamilton before they earned their moves to Wigan Athletic, where they would enjoy Premier League football and an FA Cup final triumph. McCarthy, of course, is now at a top-five club in Everton following his £13m transfer last summer.
Brian Easton was one of their contemporaries. Following a mixed spell at Burnley, he has returned to prominence by winning the William Hill Scottish Cup with St Johnstone.
Neil remembers just how much of a leap those players were forced to make, however, in their debut season in Scotland's elite, the questions they had to ask themselves about their desire to make it; the efforts they had to put in to handle the increased psychological and physical demands.
It turned out to be the making of them. Neil senses the younger element of his squad, in particular, needs to be tested and improved in that rarefied atmosphere and that, perhaps as much as anything, is what makes his side's next 180 minutes of football such a now-or-never affair.
"If you stay at the one level, you reach a plateau," he said. "You need to play at the next level to go and test yourself again. If you look at McCarthy, McArthur and Easton, that's what happened to them.
"It was a vital part of their development as young players at the time and it'll be vital for this squad to go up a level and ask themselves: 'Can you cope? Are you good enough to do it week in, week out?'
"We've got role models like McCarthy, who's moved for over £10m, plays in the English Premier League and potentially could go to a bigger club. If he can do it from Castlemilk, why can't everybody else do it?"
Hamilton are in no position to hold players back. They need to rear talent and sell it on and Neil has been pointing out to them this week that earning their place in the SPFL Premiership will then provide the springboard they need to truly further their careers.
"The profile for the players is the most important thing," he said.
"I was talking to some of them the other day and said to them that, when you are in the Premier League, you're involved in everything. You're on Sky Sports, journalists come here and you have a profile as a player.
"If you play against Morton, there's probably about 1000 fans talking about it. In the top league, you get an opportunity to express your talents and that's all I want for our players. I want them to show everybody what they're capable of and, if they're good enough, we'll try to move them on and let them have better careers and more money."
With both legs of the match with Hibs live on television, there is no time like the present for Neil's more talented charges to show a wider audience of what they are capable.
They are up against weak, battered opposition, a team clearly struggling to get itself out of the rut that comes from a run of 19 games with only one victory.
"The momentum is with us, but we are not favourites," said Neil.
"Hibs are a huge club with Premiership players and boys on vast amounts of money compared to what our boys are earning. They are the favourites, but we are confident we can do well if we put them on the back foot from the start.
"I would prefer a one-off game. Two legs make it difficult and our players won't be used to playing in front of 15,000 people at Easter Road.
"Hibs have better players than their league position suggests, but that's where they find themselves and we've got to take advantage."
Neil has also admitted that the tide is very much against his counterpart, Terry Butcher, as he tries to stop his side's freefall.
"I wouldn't like to be in his position," Neil said. "It is hard when you are a manager and things are not going for you. We want to grab an early goal and see how they react if they do go behind. The pressure is on them. That's our game plan: to get at them and see how it pans out."