Blaze Foley (Benjamin Dickey), the dissolute country-blues singer who’s the subject of Ethan Hawke’s “BLAZE,” is about as unlikely a central character as you’re ever going to see in a movie. He’s a big, burly hillbilly who walks with a severe limp (thanks to a bout of polio) and drinks himself into testy stupors, and to say that he’s not big on verbal communication skills would be putting it mildly. His conversation, or what passes for it, is a barely mumbled series of asides, spiced with the occasional tall-tale joke, all growled out in a kind of drawling shadow whisper. (He sounds like Tom Waits, and looks like a roly-poly version of him, too.)

When Blaze picks up his guitar and sings, it’s clear that he’s got a gift, though it’s not as if the movie suddenly kicks into some enthralling high gear of country-and-western transcendence. On occasion, Blaze’s songs of loneliness and longing, like “If I Could Only Fly,” make you feel like you’re listening to some in-the-raw contempo version of Hank Williams. Just as often, he sounds like an amateur-night crooner lurching his way through a set at a local roadside dive — which, for much of “BLAZE,” is just what he is.

That aura of obscurity is an essential aspect of the film’s mystique. There really was a Blaze Foley (née Michael David Fuller), and in the years following his death (he was killed by a gunshot in 1989, at the age of 39), a handful of his songs found their way into the repertoire of country superstars like Merle Haggard, Lyle Lovett, Willie Nelson, and Lucinda Williams. During all that time, his aura has only grown. “BLAZE,” however, is about a sweetly passive and self-destructive anti-star, with a buried bad temper, who is mostly a monosyllabic layabout. He’s the hero as lug — but the thing is, this lug has heart. And the daring of Ethan Hawke as a filmmaker is that he shapes his scenes not in a conventional way but as randomly observed slivers of life that amble and glide along to Blaze’s dawdling spirit.

If the film were any less accomplished, that redneck-verité approach might have proved disastrous. But “BLAZE,” which leaps around in time, telling Blaze Foley’s story by zeroing in on a handful of disparate moments, is beautifully made. It’s an organic slice of life — raw and untidy, deceptively aimless but always exploratory. That it’s a musical biopic about a figure who spends more or less the entire movie mired in anonymity and failure is really the essence of it. Hawke has made the ultimate hipster movie. That’s a recommendation, though maybe a qualified one. “BLAZE,” artful as it is, walks a thin line between inspiration and indulgence, but the film ends up on the right side of that line.

The story, as structured by Hawke, plays like a series of extended flashbacks within flashbacks, and that’s a very smart strategy, because it keeps the rambling scenes poised and alive. A framing device is devoted to Townes Van Zandt, played ingeniously by the veteran musician Charlie Sexton (who radiates a hypnotically damaged star quality), seated in a radio studio being interviewed about Blaze, who became a friend of his when the two lived in Austin. From there, we cut to Blaze as he meets and gets to know Sybil Rosen (Alia Shawkat), the aspiring actress who became his wife. (The film is based on her memoir.)

They do not, at a glance, seem the likeliest of couples. He’s a towering and inscrutable country boy; she’s Jewish, no-nonsense, and rather petite. But they find a vibe, and move in together in a roomy cabin in the woods that serves, for a while, as their treehouse paradise. The two have nothing but each other, and that’s enough.

Hawke lets the scenes play out in real time, but he never lets the audience get too caught up in any one moment. “BLAZE” is sometimes touching, but it’s almost profoundly unsentimental. Just as we’re sinking into Blaze and Sybil’s scrappy idyll, the film will leap forward to a solo performance Blaze gave, in a hidden bar called The Outhouse, shortly before he was killed. On this particular late afternoon, his performance is being taped, ostensibly for a possible live album, but Blaze, in a ZZ Top beard and E.T. wide-brim hat, is at his mangiest. He’s an artist sliding into the skids. And then there’s his death, a murky incident triggered by his generosity and anger.

In between, the movie cuts to his one brief flash of success, when a trio of small-label record executives — played, with amusing semi-smarm, by Richard Linklater, Sam Rockwell, and Steve Zahn — approach Blaze after a gig with the possibility of signing him. He doesn’t hesitate to make a deal, but later, when he’s performing at the Lone Star in New York, everything falls apart. He’s visited there by Sybil (the two have now broken up), and his scattershot stage patter results in the crowd booing him. Still, it’s not entirely clear why he’s dropped from his label — or, for that matter, why he and Sybil fell apart. Hawke, presenting a series of snapshots, at times gives us crucial information in shorthand. He’s not interested in tracing conventional arcs. “BLAZE” is a story told on the high wire — a movie you watch without a net.

Yet that’s part of its allure. We have to put together what happened to Blaze Foley, and the movie gives us just enough clues. Benjamin Dickey’s performance is gnarly and true: His Blaze can be a charmer (especially when he’s beguiling truck drivers with his long joke about a coffee enema), but he can also be a sullen lout, and when we meet his father (Kris Kristofferson), who can’t do much but grin and ask for a cigarette from his institutional bed, we see why Blaze, in his way, is so broken. His dad was a drunk who hit him and threw away the family’s food money on bottles of Thunderbird. Maybe that’s why Blaze is so…unconnective. He’s damaged goods, though that links him up to any number of the haunted country and blues singers of the past. His songs ring out because he knows that pain.

“BLAZE” is the kind of movie that’s likely to inspire more excitement at Sundance than it does in the outside arena. The hipster quotient looms large here; in the real world, not so much. Yet as “BLAZE” went on, I found myself quietly lured into its audacious design and delicate feeling. It’s no masterpiece, but it’s an experience, one that ever so gently opens your ears, your eyes, and your heart.