Suppose you have some summer days to spare. Suppose you have a fondness for trains. Here’s the idea. Do the southern coast of Italy. Do it bit by bit, as you feel and as it comes. Not worrying too much about timetables (no one else will), or even about precise destinations. You’re not sightseeing. Just accepting the sun-struck languor of the hills and beaches, the odd mix of hospitality and indifference that characterises the locals, the general invitation to a warm, wine-fed fatalism.

Travel light. Very light. The idea is to do everything, aside from the trains, on foot. You have a small backpack with two or three T-shirts, underwear, shorts, swimming gear, washing kit. You really don’t need anything else. Your sun hat is on your head, your sandals on your feet, your shades on your nose. What we’re trying to do is divest ourselves of our ordinary obsession with organisation and control. Italy’s southern railways are peculiarly conducive to this. Tell yourself before starting: I will never complain about a train being late, or even departing early, or from an unexpected platform. I will be patient. I will be steady and slow as sunshine on a stuccoed wall.

If you have the time and inclination, you could make your way by rail and ferry to Palermo and start with Sicily (the Milan-Palermo train actually boards the ferry). There is the long line, much of it single-track, running along the north coast from Messina to Trapani. I once spent a scorching day at the cutely named Isola delle Femmine, just outside Palermo. To the south of the island there is the marvellous 2km-long tunnel that climbs in a spiral from Modica on the coast to spectacular Ragusa, a lava stream of baroque facades toppling from a high ridge into rugged valleys. And of course there’s the wonderful ride up the east coast from Syracuse to Messina, under the volcanic slopes of Etna, where Sicilian writer Giovanni Verga set so many of his short stories.

The difficult-to-find Trapani railway station in Sicily. Photograph: Getty Images

But Sicily is difficult. Using trains here is considered eccentric. There’s no line to link Trapani in the west to Agrigento on the south coast, and crossing the island north to south requires seven hours and three changes to go 190km. Much of the network was built in the 19th century to bring sulphur and salt down from mines in the mountains and makes little sense now. I remember once in Palermo Centrale, puzzled by the mismatch between the information on the ticket machines and that on the departure board, I asked a railway worker if there actually was a train to Trapani that day. Without taking his cigarette from his mouth, he advised me that if he were going to Trapani, he would never use the train.

So here’s an easier solution. Instead of attempting Sicily, take the line that snakes round the bottom of Italy’s boot, all the way from Reggio Calabria on the western toe (linked by trains to Milan) to Taranto on the eastern heel. That’s about 500km of single-track railway. As long as you keep the sparkling sea to your right and thirsty vegetation to your left, you can’t go wrong.

Your daily routine is as follows. Breakfast in the hotel. Morning stroll and swim. Lunch under sunshades along the seafront. Train in the mid-afternoon, to kill the hottest hours. On board you can use your phone to book a place in whatever upcoming town takes your fancy – nothing beats an unplanned adventure. Melito di Porto Salvo on Calabria’s south coast, perhaps, where Garibaldi landed in 1860 to start his triumphal march to Naples. Or Brancaleone-Marina, further round the coast, where novelist Cesare Pavese was sent into internal exile for anti-Fascist activity in 1935. He complained bitterly, but it’s hard to imagine a bluer sea or whiter beach.

You’ll find the small stations mostly deserted. The locals prefer their cars. It hardly matters that the ticket machine is out of order because you’ve sorted yourself on the internet. A single, diesel-driven carriage appears in a shimmer of August heat. It may be only 10 minutes late, but it looks like it’s coming from another age. Inside, a rattling air-conditioner just about keeps the temperature bearable. A couple of hawkers with cheap merchandise to sell on the beach get their packs stuck in the swing doors. One is wearing five blue sombreros on his head. A group of 10-year-olds run up and down the aisle. No business travellers. No other tourists.

The narrow alleys of Crotone. Photograph: Alamy

Crotone, facing east across the Ionian Sea, is a surprise. The huge chemical factory to the north – one of the endless failed attempts to industrialise the south – closed in 1990. No bus awaits arriving passengers. Your half-hour walk into town is hot work. But when you get there, what rewards!

The place to stay here is Hotel Concordia (doubles from around €70), where New Grub Street writer George Gissing resided in 1897, and fellow novelist Norman Douglas 10 years later. From their descriptions of the railways in their respective travel books, By the Ionian Sea and Old Calabria, it doesn’t seem much has changed. Having seen your booking made an hour before, the manager is at the door to greet you by name as you approach. He recognises an Englishman a mile off, but can’t believe you don’t have a car. “Nobody travels by train.”

The centre is a labyrinth of narrow alleys climbing up and around a steep conical hill, each thread of street crisscrossed above with drying laundry and inhabited below by folks playing cards and drinking wine outside the bead curtains that protect their doors. At a corner a man is sharpening knives on a grindstone he turns with pedals and a chain.

At the top of the hill a castle houses a museum of Greek artefacts, for you are now in Magna Grecia, that part of Italy colonised by the Greeks in 700BC. You can wonder at winged horses, pretty mermaids, a tiny rabbit-shaped container that once held cosmetic oil for a woman’s skin. Brightest of all is a gold diadem fashioned into a circle of leaves and berries, emblem of the goddess Hera, whose ruined temple boasts just one standing column on the cliffs to the south of the town.

Come early evening, lying on your back in the calm, warm sea, taking in the great sweep of the bay, it’s not hard to imagine the Greek galleys at anchor in their scores, conquering and trading as the British would do a couple of thousand years later. Right now, though, there are just a few rusty fishing boats and the tinkle of a band grinding out 1960s covers in a beachside bar.

Corigliano Calabro. Photograph: freeartist/Alamy

And so onward into the Bay of Taranto, the big, squarish arch under Italy’s boot. First north-east to Corigliano Calabro, then north-west to Taranto itself, where a much grander collection of Greek art awaits. The sway of the train and play of light and shade induce a pleasant stupor. Empty sands and blue seas. Bleached-white riverbeds. Mile after mile of olive groves and kiwi plants. Stazione di Torre Melissa. Vineyards. Grey rock promontories. Stazione di Cirò. The train guard’s whistle. A squat tower on a low hillside. Cacti and scorched grass. Stazione di Crucoli. Graffiti: Ti penso sempre amore mio (forever thinking of you, my love). Anna e Giulia troie (scrubbers). No sign of railway personnel anywhere. In English someone has scrawled: “Boys 1978. Wanderers Everywhere.”

Stop wherever you want. Or don’t stop. Depending how many days you have. But don’t miss the old quarter of Taranto. Just a few hundred metres from the station, you cross a swing bridge that divides a huge inland lagoon to the left from the open sea to the right and at once you’re in an antique metropolis of dark narrow streets and people sitting out on kitchen chairs looking in through the windows at their own TVs in rooms whose walls are nothing but bare stones piled up centuries ago. Men and women call to each other across and along the streets with strange cries and coded whistles, a fluid repertoire of gestures that very probably haven’t changed in many generations. I know of nowhere in Italy where an ancient past seems so alive.

Taranto. Photograph: Getty Images

Do you want to go on? There’s no line now along the west side of the bay to Gallipoli and Santa Maria di Leuca at the tip of Italy’s heel. But you can take the train toward Brindisi, get off at Francavilla Fontana and link up with the Ferrovie Sud Est, a local network that somehow contrives never to run along the coast but will take you to Otranto, and Galliano del Capo, just a short bus-ride from the wonderful Santa Maria.

Still, if Italian State Railways tried your patience, Ferrovie Sud Est will transport you into a surreal heat haze of unexpected connections and sudden cancellations in which you will very likely spend hours entirely alone with a garrulous ticket collector delighted to have found someone to talk to. Everywhere signs inform you of the generous contributions of the ever beneficent EU. In any event, if you’re returning home via overnight couchette from Lecce to Milan, make sure you set off with a good few hours to spare. Then put your head down on a Trenitalia pillow and let the rails lull you into a last Mediterranean reverie.

• Trenitalia.com has information on the Italian train network, and tickets can be bought online with the Trenitalia app (ignore the invitation to log in and register and continue your purchase as a guest). For details on travel to Milan via Paris from London, visit loco2.com

Tim Parks is author of Italian Ways, on and off the Rails from Milan to Palermo (Vintage, £9.99), available for £8.79 at the Guardian Bookshop

Browse the Guardian’s selection of some of the world’s best rail journeys on the Guardian Holidays website

This article was amended on 9 May 2019 to correct the statement that only Italian residents could buy tickets via the Trenitalia app