The Yorkshire first-team coach played in an era when Australia were renowned not only for their exceptional skills, but also for their ability to never know when they were beaten.
It was a spirit epitomised by wicketkeeper Adam Gilchrist, who on those rare occasions when the top-order failed, could turn a match on its head from No 7.
Whenever Australia were in trouble, it seemed that somebody – a Gilchrist or otherwise – would contrive to dig them out of a hole and put the pressure back on their opponents.
Yorkshire have displayed similar qualities in the County Championship this season, never more so than in their last match against Durham at Scarborough.
The champions were in trouble at 95-9 in their first innings before a last-wicket stand of 67 between Tim Bresnan and Ryan Sidebottom lifted them to 162 all-out, Yorkshire then bowling out Durham for 156.
And they were in the mire again at 79-5 in their second innings, a lead of just 85, before Glenn Maxwell and Adil Rashid shared in a sixth-wicket stand of 248 that helped Yorkshire to a final total of 440.
Liam Plunkett and Adil Rashid then took seven wickets between them as Durham were dismissed for 263, the hosts prevailing by 183 runs to record their sixth successive Championship win.
Asked whether a comparison could be drawn between Yorkshire’s resilience and that of Australia in Gillespie’s time, the former fast bowler said: “Yes, you could say that.
“Someone like an Adam Gilchrist would come in and play a great counter-attacking innings, and we’ve seen a lot of that type of fight from our lads this season.
“Tim Bresnan stepped up in the first innings at Scarborough and got crucial runs, and then Glenn Maxwell and Adil Rashid took the game away from Durham with a brilliant counter-attacking performance in our second innings.
“It’s pleasing that people are stepping up to the plate, and we’ve seen it many times now from our players this summer.”
The general consensus is that Yorkshire have not yet played quite as well as they did last year, when they won the Championship for the first time since 2001.
However, they have a better record now than at this stage last summer – currently eight wins and three draws from 11 games – and it would be the cricketing equivalent of Devon Loch’s failure to win the 1956 Grand National if they slipped up from here and did not go on to take back-to-back titles.
Gillespie believes Yorkshire’s resilience stems from the players’ thirst for success and also the trust they have in each other and the meticulousness of their preparation.
He feels these give them a vital edge when the chips are down.
“We’ve held our nerve in crucial periods, at crucial moments of games, and I genuinely think it comes down to having that trust in each other and being safe in the knowledge that you’ve done everything you can to be successful,” said Gillespie.
“It’s a happy dressing room, and even when we’ve been under the pump a little bit, there’s been a calmness about the lads, and we try to instil that in them.
“They know they can be successful whatever happens.
“The lads know they can fight their way out of things because they’ve done it before, and they’ve done the work and prepared as well as they possibly can.”
Much of that freedom to “go out and play” comes from Gillespie and director of cricket Martyn Moxon, with captain Andrew Gale expertly directing events on the field.
But although those three men have played a huge part in making Yorkshire indisputably the best side around in four-day cricket, Gillespie says Yorkshire can still improve.
“We’ve won six games on the trot and some people might say how do you improve on that, but we certainly can,” he stressed. “We have to be completely honest and say that there are areas we can be better at – not least our top-order batting.
“Our top-five need to step up and get the job done, and they’re working incredibly hard to do just that.
“We’ve been lucky enough that we’ve had some fantastic, big partnerships in our last few games.
“While it’s great that someone has always stepped up, we don’t want to be leaving it to the middle and lower-order all the time, so we’ve set the challenge to the batsmen to get the job done,” he concluded.
It is a challenge issued from a position of strength.
Yorkshire are blazing a trail in the Championship again, and the worrying thing for their opponents is that they can still get better.