I'd like to dedicate this story of Taco Bill to Attica's Ben Shewry. Two years ago, the Kiwi chef whose restaurant's fame is owed to the way he tells an Australian story via plate, encouraged us to ditch our cultural cringe by embracing not just the Indigenous ingredients restaurants like his have been championing, but our ocker food identity, too. Our meat pies and Vegemite. It was a message: stop being so bloody up yourselves.

And so today we're here to celebrate Taco Bill, not Australia's most authentically Mexican experience, but certainly many Australians' first experience of south-of-the-border cuisine – albeit in cheesy Tex-Mex form and served with fishbowl-sized frozen margaritas. Ole!

The story starts in 1967 in Mermaid Beach, Queensland, where Californian-Mexican Bill Chilcote landed with the equipment to make tortillas. Only problem: in a taco-less country, demand wasn't high. So, Chilcote opened a little shop out front, what would become the prototype for the takeaway-only store launched in Armadale, Melbourne, in 1972.

But the real Taco Bill, the place you know for cheesy enchiladas and possibly some of your finest hangovers, didn't start until '74, when partners Stan Teschke and Graham Knight helped Chilcote open the 50-seater on Russell Street, Melbourne.

Back then, according to Teschke, rent was $50 a week, yet six failed businesses had previously occupied the space. Still, they were confident. Right up until they left the fryer on, a day before opening, and burnt the place down, and discovered Chilcote (a former firefighter), had no fire insurance. The rebuild was tough, and by hand, but Teschke reckons they "must have exorcised the demons, because when we opened, it took off".

If you thought Mamasita's queue up the stairs for tacos in 2010 was a phenomenon, you should have seen Taco Bill's in the '70s. Teschke says "people queued from 5pm on Fridays, drinking from their flagons". It was BYO then, no corkage charged, and competition for tables was so fierce, couples made friends with strangers to get a four-top quicker.

The good times only got looser when Australia's first slushie margarita was poured in 1981. It was the drink that solidified Taco Bill in Australian forklore. From '81 to today, if you finish the comic fishbowl size, you get a sombrero. Kylie Minogue has worn one. As has AFL player Warren "Wow" Jones. If you still doubt its resonance, Teschke was once contacted by the family of a Perth man who was "taken by a shark, and had such treasured memories of Taco Bill they requested sombreros the pallbearers".

The original menu was shorter. Flour tortillas weren't reliably available and hard to make, so there were no burritos, only enchiladas (filled corn tortillas baked in salsa and cheese); frijole dip (refried beans, made to a recipe from the mother of Chilcote's Mexican wife), Mexican chilli and king of kings: guacamole. If you think we're smashed-avo-obsessed now, back then they had a special sign to indicate whether guacamole was in the house (out-of-towners called to check), depending on whether they could get hold of the exotic fruit.

Today there are 33 Taco Bill stores, all in Victoria, and the intensity of the fiesta vibe depends on where you go. South Melbourne is a stalwart for the ad crowd. Russell Street, the OG, with its flower-painted door, sparkly sombreros and poncho decorations, is as cosy and kitschy as ever. Collins Street has the best tequila selection. A franchise in Altona North, with its mariachi-band-meets-house-beats music, its big screen TVs and laminate tables, is a pale comparison, and yet in its tackiness possibly comes closer to dining in Mexico than the neon-signed, blond-wood establishments from the 2010-2014 new Mex wave.

Is it any good? Tomato salsa with tortilla chips to start has proper tang. And even if there are no three-days-in-the-making moles or in-house tortillas, trashy good taste buttons are still pressed in your brain when those spiced beans meet chopped tomatoes, iceberg lettuce, sizzling platters of chicken with capsicum and onions and a whole boatload of sour cream and shredded cheddar. Even if said cheddar doesn't melt in the microwave if you take the leftovers home.

Since new Mex, they've adjusted with a more share-friendly menu and (having gone with a vego pal) I know you can get decent spinach and potato enchiladas; crumbed jalapeno bombs with cream cheese centres (stiff, but acceptable with beers) and bean-based burritos with all the trim.

A proud food footprint is the nachos, layered with ingredients throughout rather than just topped. Margaritas, in multiple flavours from strawberry to Blue Curacao, and served in "I'm driving" to sombrero-winning size, are very sweet and could possibly use an extra shot, but the silliness has some modern appeal.

Mate, it was the one restaurant request of Pink on her last tour. Amen Oz-Mex. You bloody ripper.

Address 142 Russell Street, Melbourne; various locations, tacobill.com.au

Open Varies; check the website.

Est. 1974

Famous diners Pink, Lee Trevino, Kylie Minogue, Hamish Blake and Andy Lee.

Signature dishes Nachos, fishbowl margaritas, fajitas, guacamole.