They may be singular men but Martin O'Neill and Roy Keane have, of course, been shaped by rather more than the impetus of their own fierce natures.
Everyone knows the heart of their deepest competitive origins, the extraordinary force of their late manager at Nottingham Forest, Brian Clough, but who can answer with any certainty the question invited mostly strongly by the FAI's extraordinary gamble on a partnership that is being variously described as ice and fire and the dream ticket?
It asks simply this – can the Clough (below right) legacy, so filled with outrageous conviction and success when he was winning league and European titles, still have any relevance to the cause of the Irish team so far beyond one man's grave?
If it should be so, if between his disciples there is indeed the significant impact of an inherited, hoarded chemistry on which they have both placed so many of their separate football principles, we can only wonder again at the extraordinary meaning of Clough's tumultuous career.
For some of us, though, such an outcome would be somewhat less than astounding. This would be especially so for anyone who happened to be at the Derby's Baseball Ground 40 years ago when the civil war between the crusty old club chairman Sam Longson and the firebrand young manager had reached breaking point.
A group of players led by goalkeeper Colin Boulton marched down the main corridor.
Boulton was carrying an axe. He said the players were going to knock on the door of the directors' room and demand to know why it seemed that their manager – the best manager in the game who had so quickly landed the First Division title and carried an ill-considered club to the semi-finals of the European Cup – was about to leave. The axe was to hack down the door if the directors refused to respond.
This may, of course, be no more than a flashback to another world – one from which such brimming passions would look entirely out of place in today's football, where the primary loyalty seems to be the viability of the next contract.
Indeed, it might be said that O'Neill's exuberant nature, the intensity of his touchline performances, and Keane's unswerving belief in his own authority, are already at odds with a new game.
O'Neill appeared to lose his players at Sunderland, while Keane's resignation there and his departure from Ipswich Town seemed to speak of a man disenchanted by the style and the mores of the modern player.
Yet the FAI have made their act of faith and if the reaction has been ambivalent, no one can say that it is one bereft of dramatic possibilities.
Clough's supreme ability was to make players believe they were better than they were, and then have them produce European Cup winners' medals, and if this is not the biggest challenge that looms before O'Neill and Keane, and which eventually proved too much even for the old, masterful hand of Giovanni Trapattoni, it is difficult to imagine what is.
Certainly it is impossible to see either O'Neill or Keane gently massaging the egos of such as Stephen Ireland, Darron Gibson, Shane Long or James McCarthy.
However, pointing out the possibility of achievements that might lift their careers on to an entirely different level would be brusque, inevitable work. Something not to be laboured over, perhaps, but presented as an option worth pursuing. Such players will surely be given the opportunity that Clough once granted to such supreme over-achievers as John O'Hare and John McGovern.
When Clough brought those key men from Derby County to Elland Road in his brief and catastrophic reign at Leeds United, players of the natural-born ability of John Giles, Eddie Gray and Billy Bremner were nonplussed, even aghast. But then, when Clough regained his nerve at Nottingham Forest, both ill-considered men prospered again at the highest level of the game.
That was Clough's genius, a capacity to inject a transcending belief into players who had previously struggled for such belief.
When Keane made his last throw at keeping the Ipswich players within his influence, he was candid about how his thoughts turned back again to the style of Clough.
"Cloughie punched me but it's good to go a bit mad," said Keane. "He was dead right. It was the best thing he ever did for me. It's good to get angry. If people upset you and you don't get angry you're in the wrong game. I don't throw tea cups around. I'd rather throw punches."
It's an instinct that will plainly have to be curbed in the Irish cause and perhaps Keane learned the dangers of excess while going down at Ipswich. But if anyone is going to bring a little bit of meaningful swagger into the dressing-room, who better than Keane?
If O'Neill has a more statesmanlike touch, in his emotional, quirky way, he may well benefit from the ferocious spirit of a No 2 who knows well enough that he has entered a pivotal stage of his football life.
Which Republic player would have the nerve, temerity even, to challenge any assessment of his performance by Roy Keane? Here, surely, a great force of Republic football is recent enough to guarantee an authentic impact.
Before his breakout in Saipan, before his rage there boiled out of control, he had, after all, carried the Republic to the World Cup. While nursing injury, he ran the much fancied Dutch to a standstill. He booked the tickets to the Far East. Now the Republic want to invest again in such extraordinary will.