At the Scottish Football Writers Association's annual Player of the Year dinner in May 2000, the pugnacious Dutchman received the Manager of the Year award and ended his acceptance speech with a remark so jolting that some members of the audience had to ask their fellow guests if they had heard him correctly.
"Thank you, see you next year!" was Advocaat's chirpy sign-off, an obvious indicator of his expectation of retaining the title on the back of another season of domination. Rangers at that moment were in possession of the SPL championship and the Scottish Cup, having won the former by 21 points and thrashed Aberdeen 4-0 in the final of the latter.
Advocaat's self-certainty was never in doubt, but applying it in practical terms in the previous two seasons had been made immeasurably easier by the disarray of Rangers' fiercest rivals, Celtic, under the stewardship of, respectively, the venerable but soft-centred Dr Josef Venglos and the abortive double act of John Barnes and Kenny Dalglish.
In delivering his startlingly presumptuous tag line, Advocaat was not to know that, within a matter of three weeks, Martin O'Neill would arrive at Celtic Park. The Irishman's regeneration of the Parkhead side, through a combination of personal charisma and the astute recruitment of powerful figures such as Chris Sutton, Alan Thompson, Neil Lennon, Didier Agathe and Joos Valgaeren, would prove so irresistible that, by the end of that first season, all three domestic trophies would be placed in the Celtic Park showcase.
It was, at the time, impossible to escape the impression that Advocaat had not distinguished himself in the matter of handling his first serious challenge. The similarities between his first three seasons at Ibrox and Strachan's at Celtic now are unmissable.
This is not to suggest that neither Advocaat nor Strachan deserves credit for their productive work during those first two campaigns. Even if there was a weakness bordering on somnolence about Old Firm rivals who would have been expected to offer a more telling threat, both managers still had to demonstrate they had what was required to take advantage.
If there is a difference between Strachan now and Advocaat then, it is that the present Celtic manager has had to try to sustain pre-eminence while satisfying his directors' insistence on maintaining impressive financial returns. Much criticism has been directed at Strachan over the signing of "expensive flops" such as Massimo Donati and Jan Vennegoor of Hesselink, but that is based on a rather parochial definition of "expensive".
Donati continues to be labelled a 3 million midfielder by the media, but, as Strachan has said frequently, he cost two million euro, the exchange rate at the time making his fee 1.3m, around 700,000 less, for example, than Rangers paid Hibernian for Kevin Thomson.
At 3 million, a European striker such as Vennegoor of Hesselink would be considered cheap even by a middle-order club in the Coca-Cola Championship in England.
In the business of keeping his board sweet, Strachan has been an unqualified success, and it is hardly surprising that his employers hold him in such high esteem. In the process, however, he has almost certainly had to limit his own ambitions, as a consequence damaging his image and his credibility.
In Strachan's third season, Walter Smith's resuscitation of Rangers represents the kind of challenge made to Advocaat by O'Neill and the Celtic manager is having difficulty in coping. To this observer, his most serious imperfection in recent weeks has been the failure to recognise early enough that the form of some of his most productive players – most notably Aiden McGeady, Scott McDonald and Scott Brown – was on the wane, and to take remedial action.
Strachan has said often enough that he does not believe in squad rotation for its own sake and that he would, where possible, field what he believed to be his strongest team in every match. That is a sound enough principle as long as those selected are maintaining a course that will lead to honours. Now the league championship is the only one left and, with ten matches remaining and a three-point deficit to overcome, it is clearly a feasible objective.
In the event of failure to land a third successive title, though, the clamour for the removal of the manager, already heard on a daily basis and from a substantial number – if not a pronounced majority – of the club's followers, will become much more intense and may be reflected in a decline in season-ticket sales. Nothing impacts on directors more forcefully than lost revenue.
But Strachan has been regarded with suspicion by many Celtic supporters since the day he succeeded O'Neill and even a third successive championship – an achievement not seen since Jock Stein's omnipotent team of 40 years ago – would, in all probability, do little to lower the temperature of the hostility.
Even the revered O'Neill failed to complete the hat-trick of titles. But, reflecting on the last day of the season in 2003, when Celtic were pipped by Rangers on goal difference, there is no recollection of a concerted will among the club's supporters to have him tarred, feathered and run out of town.