There are times when Stuart Baxter surveys the agonies surrounding South Africa’s football team and asks himself whether the benefits really add up. “It’s not one of those you get used to,” he says. “You’re constantly wondering if it’s worth it. Constantly.”

It is easier to answer that question during a week when, against all odds, Bafana Bafana have hauled themselves back among Africa’s elite. Baxter calls South Africa “a country of extremes” and he should know, given that he is two years into his second spell managing the national team. On Saturday night the dial swung to paroxysms of euphoria as they outplayed Egypt, host country of the Africa Cup of Nations, in front of a baying home crowd and reached the last eight with a 1-0 win. For the 65-year-old Baxter, taking South Africa through to next Friday’s final would be the pinnacle of a globetrotting career that has never been defined by his Anglo-Scottish upbringing.

“Winning this would be the biggest,” he says, with Nigeria posing the next challenge in Wednesday’s quarter-final. “Without sounding egotistical I think this would represent a massive personal victory for me, partly because it’d be coming far more quickly than it should and partly because this is such a big tournament.”

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It was 1996 when South Africa, only four years out of a lengthy Fifa suspension and still buoyant in the early stage of Nelson Mandela’s presidency, won their first and only Cup of Nations. Baxter has brought Mark Fish, their defensive cornerstone back then, into his backroom staff to maintain a connection but he is at pains to point out that so much has changed since then. At that time Bafana Bafana, managed by Clive Barker, could ride the wave all the way home; these days they face a smothering pall of negativity that he believes places unrealistic demands on the sport’s role.

“The whole country was full of optimism in ’96,” he says. “Full of hope and belief in the future. I think the team reflected that hope. When we beat Libya to qualify this time, the sports ministry wrote to me and said: ‘You’ve given the country hope’, and for me that’s where all this negativity stems from.

“If the country is dependent on a result by the national team to give it hope, we fail. We can give it hope for five minutes, but every defeat is met with such negativity because on wider level those hopes and dreams have been flattened. There’s too much going wrong in the country: getting the electricity shut down every day, the water shortages, the unemployment, you name it. The country’s not hopeful and they’re in a mental stage of depression; I think that gets reflected. They cannot accept any more negativity so one bad result is met by a tirade.

“We can’t give the country hope. We can’t. Only temporarily. I’m just happy we can give them a night off where they can wear the shirt proudly.”

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South Africa lost to Ivory Coast and Morocco during the group stage, squeaking past lowly Namibia in between, and only reached the knockouts on goal difference as one of the best third-placed sides. The dissenting voices were deafening at that point; Bafana’s early matches had been turgid, although Baxter points out that their preparation for this tournament verged on the disastrous, with funding issues seeing their schedule decimated and only one friendly, against Ghana, eventually being played. An already young, reconstructed squad arrived in Egypt badly undercooked and Baxter says their performance against the hosts, in which they obeyed his instructions to play an aggressive, attacking game to the letter, was the kind that banishes any weariness.

“That’s basically why I’ve hung in there, because the players have shown such an interest in wanting to be better, such a genuine pride in themselves when they get it right,” he says. “They’ve been so loyal and patriotic that I’ve always gone that extra mile.”

Baxter is used to doing that. His story is well told by now but a quick refresher course in his life and times underlines what a journey it has been. He has coached in eight countries, won titles in Sweden with AIK and South Africa with Kaizer Chiefs, bitten his lip when fired after two games in Turkey and contributed significantly to football’s explosion in Japan. Were it not for the Midlands inflection – Baxter was born in Wolverhampton – it would feel like a chat with Roy Hodgson, as much for his urbanity and unaffected studiousness as for his winding road here. But unlike Hodgson he has never heard a loud clarion call from home, despite a few offers earlier in his career.

Facebook Twitter Pinterest South Africa celebrate during their win over Egypt. Photograph: Samuel Shivambu/EPA

“As it’s moved forward there hasn’t been the opportunity, and that’s because I fall between two stools really,” he says. “I’m not the exotic foreigner and I’m not the big-name English knight in shining armour; I’m neither the José Mourinho nor the Frank Lampard, and the game in the Premier League has become about perception.

“I’m not saying that’s the alpha and omega of it, but it’s why I’m realistic to know I’m not going to have a queue of people saying: ‘He’s won leagues all over the world and he’s a Brit, let’s bring him back.’ I’ve become a little, not exactly cynical, but non-expectant. When the phone rings it’s from other places: I’m exotic and attractive there but back home I’m not.”

He fancies another crack at the Champions League, in which he competed with AIK, but feels confident in his capacity to set down roots anywhere in the world and describes himself as “pretty easily transportable”, moulding himself to the project at hand. “I’m not this instructor going round the world teaching football according to the theories of Stuart Baxter,” he says. Perhaps there is an extent to which, in an era where philosophies and grand visions tend to seduce more than sheer practicality, that has held him back too.

Not that there will be any sense of regret when South Africa walk back out at Cairo International Stadium, the venue stunned into dumbfounded silence by Thembinkosi Lorch’s 85th-minute winner those few short days ago, to face Nigeria. “We have to do it as underdogs again,” he says. “They are one of the best, but if we can put together a gameplan that gives them the problems we gave Egypt then we have a chance. At this stage it sometimes takes on its own life. The difference in the squad now, the belief they have, is absolutely night and day.” Dawns like that are why, for all the brickbats and moments of doubt, Baxter comes back again and again.