South by Southwest rightly prides itself on being the trendiest of festivals. It's all about flipping the script and pushing the envelope. Breaking the mould and blowing the doors off. Yet the two hottest tickets this year were for seminars by sixtysomething white men who came on stage with nothing more hi-tech than a microphone.

Bruce Springsteen is pretty easily explicable. Jeffrey Tambor? Maybe a little less so. The man best known for brilliant turns in a couple of cult TV shows (he was narcissistic sidekick Hank Kingsley in Larry Sanders, cracked patriarch George Bluth in Arrested Development)? The man who pops up for big-screen cameos when you're least expecting them (lately: The Hangover, Paul, Win Win, Mr Popper's Penguins)?

Sure, he has been doing the chat-show circuit in the US this past week to promote his latest sitcom, Bent (no relation to the Nazi homosexual persecution play – it's an Amanda Peet vehicle in which she may or may not go to bed with her builder). But, still, that doesn't quite account for the hordes who poured through the doors at the Austin Convention Centre a fortnight ago for his annual Acting Workshop. Outside, those refused entry crowded around monitors. Inside, Tambor turned delegates into disciples, iPads enjoying a rare moment of sleep as their owners hung on his every instruction for the two hired actors (a bit of a MacGuffin, this – the workshop is really an extended pep-talk in optimistic living).

"Those people were hungry!", he says a few days later at a cafe in Pacific Palisades, the pristine LA suburb in which he lives with his wife Kasia, and their four children, all under eight (including two-year-old twin boys – he also has a 36-year-old, Molly). He taps his coffee spoon with pleasure. "They like a live experience. We all do." They seemed unusually earnest, I say, and so trusting. "Yes. And I hate blasé. I can't stand blasé."

Tambor describes himself as "an instinctual teacher. I like to help people. I talk straight at 'em. Everybody needs a kick in the ass. It's about confidence. About knowing not to falter. It's really frightening not to know what you're going to do when things go awry."

It's pumping stuff. Up close, Tambor even looks like a personal trainer. At 67, he is surprisingly built (his father was a prizefighter), sports an inside-out red sweatshirt with seams snipped off, Rocky-style. He's been doing his workshop for five or six years, with a break a couple of years back, when he took time off from it and from his day-to-day teaching obligations: "Right in the middle of class I turned to my students and said, I think I'm done for a little while. I want to go home and spend this time with my babies. It just hit me that I'm not all here; I'm not giving you everything I have."

It's a level of commitment he tries to apply to his private and professional life, and something he advocates for his students. What complicates things is that this is in tandem with another mantra: "fuck 'em".

"It's a very attractive attitude. Our best actors have it; the Vanessa Redgraves, the Al Pacinos, the Helen Mirrens, the De Niros. Bang! It's there. This is how it goes."

He had that sort of savoir faire early in his career, he says. "And then they start paying you thousands of dollars. And you think: ho ho! I have to really work at this! I have to have some sort of angst. And I come from a Russian/Hungarian/Jewish parentage and my dad drilled into me the sort of Van Gogh thing of it having to cost and your having to suffer."

Jeffrey Tambor (right) in The Larry Sanders Show

Tambor grew up in San Francisco just after the war. His father advised him to take up golf to aid a career in business, and to always check the bill in restaurants (Tambor says that he is careful to hand the bill back with payment without looking. "Well, I did till recently, But I do have five children"). His mother was preoccupied with her son being well-liked. He loved them both very much, he's eager to emphasize. As a child, he was initially gregarious, he says, before a bilateral lisp meant he took to observing from the sidelines.

"I became very conservative and afraid to leave my block as a kid. Getting that magic back interests me."

Tambor's motivational rhetoric is clearly nothing if not from the heart. Vultures perch on his shoulders every day, he says, cawing at him with bad vibes. "You just have to not talk to them; you can't inhale that stuff." What do they say? "Oh, so you're a public speaker now! Oh! I see!"

Indeed, the more he talks, the more it's evident that Tambor flip-flops between confidence and something more rocky. On the one hand, he always thought he'd be successful, he says, and he's a devoted cheerleader for his profession: "Being an artist is a whole way of being. I'm very protective of that. It's a heroic journey; it's a struggle and you have to practise it day by day. You can't just do it on impulse. Who the fuck is inspired? No one. The toughest thing in the world to do is get up at 6am and open that script. You never want to. You want to call Rome, clean your carpets, interiorise your car." His dread of facing the music means he begins books on chapter two, and starts articles backwards.

It is genuinely a complete pleasure to talk with Tambor – but one that is easy to misread. Your natural reaction on looking at that long, poker face, on hearing those sherry-ad tones, is to laugh. As time passes, it dawns on you how inappropriate a knee-jerk giggle may be.

He gets that a lot. "I'm a very serious person. People say to my wife: oh you must sit and laugh... she rolls her eyes. I do have access to humour but …"

In fact, this is another example of Tambor's self-deprecation. He is very funny, shares a playfulness and a charisma with his Arrested Development alter ego. The actor Michael Cera tells a story about how, when he first met Tambor on set, he introduced him to his mother. "I'm not interested in meeting your fucking mother," Tambor replied, before walking to the other end of the room, getting a coffee, coming back and kissing her on both cheeks. He tells me about bashing shopping carts with a grumpy looking woman a few weeks ago in the supermarket, just to get a reaction (she laughed - "mission accomplished").

Jeffrey Tambor (left) in Arrested Development. Photograph: AP

But the key quality that emerges in the flesh is that same naked, endearing eagerness to be accepted that he conveyed so brilliantly in Larry Sanders. Unlike Hank, Tambor need not worry that he's a talentless buffoon, but that doesn't mean he doesn't fret about it.

His confidence modulates with the size of his audience, he says. If it's a crowd, he's in control. "But I'm not that great one-on-one. I'd rather read or be with my family. I don't like schmooze or small talk. When someone sits down and talks to me about their problems, I love it. Let's get to it! Wouldn't it be really wonderful if we could all just talk about what was really on our minds? I remember once saying to my friend Henry Winkler when we were having coffee: you're bored aren't you? I'm so, so worried people aren't interested."

Tambor is sensitive to the extent that he cried when he picked up his children's library cards, so comforting does he find books. He seems to hanker after footholds – a dabble with Scientology has come to an end, and it seems fair to say that the experience has contributed to what he calls his "wounded position".

He won't even ever watch himself on playback after he has shot his scenes. "It's not about being old or bald, or having a double chin, or this nose. It's a different hemisphere of the brain. As I'm talking to you, if I saw a picture of what I looked like I would shut up and leave."

A little while and a big hug later, he does, home for supper, early to bed, happy to wake, fingers crossed.