I’m usually not picky about what I wear to go hiking, but for this walk I purposely chose a bright orange T-shirt – in case someone had to come looking for my body.

I was planning to walk alone up a scrub-covered cliff face in a remote part of the Ionian island of Ithaca: locals said there was no path any more, after serious earthquake damage in the 1950s. Ithaca is known as the home of Odysseus, to which he returned after 10 years of adventures. It lies in the shadow of larger Kephalonia, which has grown rich on Captain Corelli, an airport and some fine beaches.

An experienced walker of unpredictable Greek island paths (but not a rock climber), I was doing this hike for three reasons. First, I’d been employed to check all the walks in author Jane Cochrane’s latest book, Walking in the Footsteps of Odysseus. Second, in mythology, Telemachus, son of Odysseus, landed secretly at Pera Pigadi after returning from a fruitless search for his absent father and then scaled these rocks, called Korakos Petra, to meet the family’s loyal servant Eumaeus (and a mysterious visitor who turned out to be Odysseus in disguise). And third? Because they said it couldn’t be done …

It was at Eumaeus’s house, on the plain atop the cliff, that Odysseus plotted how to kill the 100-plus suitors who had been bothering his wife, Penelope, for close on a decade.

Jane Cochrane is a retired architect who has had a home on Ithaca since the 1980s. I knew all about her and her late husband, Alec Kazantzis, from her 2019 autobiographical book Odysseus’ Island; she knew that I’d spent a lot of 2020 following the post-Troy route of Odysseus around Greece and Italy.

For her new guidebook to Ithaca, Jane aimed to lead the visitor to places associated by scholars with the words of Homer, whose descriptions in The Odyssey are so geographically accurate that she was convinced he knew the island first-hand. The plan was for us to combine forces to follow in the steps of his protagonists.

Jane had no intention of risking Korakos Petra, though. “But if you want to give it a go,” she told me, “I can double back, get my car and meet you at the top!”

So we hired a boat to take us out around the coast to Pera Pigadi. Landing here is tricky. Our skipper, Pierre, sailed as close as he could then, stripping to his underwear, jumped overboard and pulled the boat in as far as possible. I waded ashore after him, holding my clothes above the water. I looked up at the 250-metre white cliff towering above skirts of wild greenery and a deep, deep ravine; it was like something from The Lost World.

According to legend, a hunter called Korax fell to his death here, and his grieving mother, Arethusa, hanged herself next to a nearby spring. I had no intention of joining Korax, but I didn’t know at this point how close I would come to doing so.

In hi-vis T-shirt, jeans to protect my legs, and with soaked underwear tied to my stick to dry, I made my way up a footpath to Arethusa’s spring, a lovelier spot than its dark history suggested. But from there to the top there was nothing to help the hiker – definitely no path.

I had planned to fill my water bottle from Arethusa’s deep natural well – but its rusted bucket leaked most of its contents before I could haul it up. After half a dozen tries I managed to get a decent amount, but another thing I didn’t know was that the bottle and I were not to be together for long.

Beyond the spring, the rock wall rises like a fortification, with barely any footholds or handholds. The ravine was to my left and I had to go up and over it at its narrowest point in order to carry on to the top. As I inched my way up, I kept tossing my bottle and stick up ahead of me to leave hands free for holding on. I failed to resist the temptation to look down. Not far below were the tops of tall trees growing in the ravine; I couldn’t see how far it was to the bottom but it was a lethal-looking distance. More than once, as my fingertips held tight to almost nothing, I had that dread feeling that I was about to fall – and that before I hit the bottom, I would feel exceedingly stupid.

The water bottle rolled off a ledge and past me at a moment when I was above a sheer drop and dared not free a hand to catch it. I watched it bounce in slow motion into the depths and disappear.

Getting over the ravine was the most dangerous bit of the climb. After that it was tough but not life-threatening. Somewhere on the ensuing long half-walk, half-crawl through spiky undergrowth and tangled trees, I realised that my stick – and my underwear – had disappeared. I was not going back for them.

Every so often, as I continued up through dense thickets, I stumbled on what looked like the remnants of paths. These would always lead in the direction I needed – but sadly didn’t last for long. I rejoiced when one of the longest and clearest bits of track started near the top and took me all the way up to the summit.

I am convinced there was once a network of paths here, used by farmers going from the plain to the spring and the sea and back. A fit ancient Ithacan could have bounded up Korakos Petra in much less than the two hours 25 minutes it took me. Young Telemachus could definitely have done it.

Jane firmly advises others not to follow my example; her guidebook includes a safer but longer way of exploring this area, plus a dozen other walks that we checked together. She gives maps and instructions for getting to the beach at Dexia, where Odysseus finally came ashore; up to the Cave of the Nymphs, where he hid the treasure he returned with; south across the island to the plain where his livestock grazed; to the cave where Eumaeus spent nights guarding his herd from wild dogs; all the way north to the Mycenaean remains of the Palace of Odysseus; and down from there to the Melanhydros springs whose waters Penelope and her maids might have used.

Along the way her book encounters 19th-century archaeologist Heinrich Schliemann, who barked up the wrong hill in the 1870s; pioneering Sylvia Benton discovering wonderful things in the 1930s; and wife-and-husband archaeologists Litsa and Thanasis Papadopoulos excavating and finally identifying the Palace of Odysseus in 2010. Jane is the latest in a long line of Ithacan heroes … and it was an honour to be with her for this latest part of the island’s journey through history.

Walking in the Footsteps of Odysseus (£9.99) can be ordered at janeocochrane.co.uk. The author will be in conversation about the book on 28 April, 6.30pm, at Paddington Library, London. More information from ithaca.gr and rentaboatithaca.com