Searching for Sugar Man, Malik Bendjelloul, 86 mins, (12A)

Think about your favourite obscure pop star. And by "obscure", I don't mean semi-famous for a week, then forgotten; I mean, never discovered in the first place. As in: only sold six copies of their album, one of which your mum found in a car-boot sale in 1974. Now imagine an alternative universe in which that artist happened to become inconceivably huge: Stones big, Dylan big. Imagine that for a moment – and now Google the folk singer Sixto Rodriguez.

Rodriguez, we learn from documentary Searching for Sugar Man, was just another among multitudes of failed acts in his native USA, but by some freak twist became phenomenally successful in South Africa. His drug-dealer song "Sugar Man" was so popular that if your surname happened to be Segerman – like a player in this film – your mates would dub you "Sugar Man" or just "Sugar" and everyone would get the reference.

Malik Bendjelloul's film, evocatively pitched as a detective story, tells how a Mexican-American singer- songwriter made two albums in the early 1970s that bombed in the US, but that somehow touched a nerve in South Africa. His first album Cold Fact was embraced by young white liberals as a covert bible of anti-apartheid rebellion. A singer with a Hispanic name singing about bringing down the system, peppered with sex and drugs references – this was as good a rallying call as any under a repressive regime, that is sketched concisely in archive footage.

It's one of the mysteries of music fandom that in the 1970s someone could sell a lot of records while having no public presence at all. Nothing was known about Rodriguez, though myths circulated: he'd supposedly set himself alight, or blown his brains out on stage after a flop comeback concert. This may say more about the 1970s South African cultural imagination than about anything else; at any rate, Rodriguez sold half a million records in that country.

Then various fans attempted to learn more about him. Some poignant facts emerge, including one that goes right to the top of the couldn't-make-it-up file: his record company dropped him two weeks before Christmas, shortly after he'd recorded a song that began, "I lost my job two weeks before Christmas."

Ding ding, SPOILER ALERT! About an hour in, we learn what happened to folk's elusive Pimpernel. He was found to be alive, well, living in Detroit and apparently very much not in receipt of the royalties due to him, seemingly lost somewhere en route from the southern hemisphere. There's a telling interview with his former label boss Clarence Avant, who's not only defensive but alarmingly cavalier about the idea that Rodriguez might have lost out on a fortune: his attitude, let's say, is very old-school music biz.

More forthcoming interviewees are Rodriguez's South African fans and (eventually) collaborators who helped raise this enigmatic phantom. His daughters also testify to him being the proverbial regular guy, a socially committed member of the Detroit community who never much cared about money or fame – just as well, as he never had the faintest idea anyone was remotely interested in him. The Sixto Rodriguez we meet today is infernally charismatic under his black hat and Roy Orbison shades, and doesn't have a great deal to say, but says it affably and with grace. It turns out he's well known in Detroit as a builder and demolition specialist, and a formidably snappy dresser. When he plays a comeback concert, in South Africa in the late 1990s, there isn't a dry eye in the house – or rather stadium, that's how big he was there.

There's some speculation about why Rodriguez never made it at home – although it seems fairly obvious that early 1970s America wasn't likely to go wild about a Latino protest singer whose lyrics had a gritty realist slant. But to be honest, the evidence of the soundtrack is that Rodriguez wasn't that great in the first place: with their over-fruity orchestrations, his tracks sound mid-1960s old hat, and his delivery is rather limited, with faux-British overtones like a raspier Donovan. Not a lost Dylan, as claimed; maybe a surrogate Gordon Lightfoot or Al Stewart. Still, it's an amazing story, with an admirably modest hero. Who knew there were second acts in forgotten singers' lives? Maybe punk-era diehards will yet see that film revealing Johnny Moped's lost years as a megastar in Latvia.