"Actually," says Amy Cheong, from Hotel Fort Canning, who is showing me round the hill, "the grave probably isn't that of Sultan Iskander because he left here to found Malacca.
"There are streets there named after him, so we can't really claim him."
But whoever is buried there, the hill was definitely the home of the island's rulers, dating back to the time when it was simply called Temasek or Sea Town.
It is almost certainly the resting place of the Sumatran king Sang Nila Utama, who gave the place its present name - Singa meaning lion and Pura meaning city - after he saw what he thought was a lion on the shore. ("Since there are no lions here, it must have been a tiger," says Amy.)
It was definitely where the first British Governor, Sir Stamford Raffles, built his house when he founded modern Singapore in 1819. And as successive governors followed his example, it became known as Government Hill.
Raffles also created a botanic garden on the hill and, while that is long gone, it now houses a spice garden where Amy was able to show me nutmeg and vanilla, chilli and ginger, lemon grass and cloves - all growing happily.
Forty years on, as Singapore began to acquire strategic significance, the British transformed the hill into a fort - named after the then-governor Viscount Charles Canning - with high stone walls, barracks, an armament store and hospital.
The main gate and a section of wall are still standing, so I was able to wander around the remains and even climb to the top of the gate where bygone sentries would have kept a close eye on the town below.
Even the Hotel Fort Canning, where I was staying, was originally built in 1926 as the British Army headquarters in the Far East. Later, as World War II loomed, they also constructed a huge underground command bunker inside the hill opposite.
It was here that General Arthur Percival planned his ill-fated defence of Singapore against the Japanese in 1942. After the British surrendered, the Japanese used the hill as military headquarters until their surrender in 1945.
The underground bunker has now been restored as a museum, called the Battle Box, where visitors can explore the chambers full of communications equipment and map rooms filled with worried-looking uniformed figures.
And an audio-visual display recreates the build-up to the Japanese victory in which, as my Singapore Tourism Board guide Toon Hee put it, "the British were bluffed by the Japanese. The Japanese were outnumbered three-to-one, but they persuaded the British it was the other way around."
To emphasise its historic links, the hotel has four archaeological pits in the floor of the foyer displaying some 14th- and 19th-century artefacts dug up on the hill; the arrival of the British is confirmed by the presence of some old bottles.
The hotel development has retained the facade of the elegant Edwardian headquarters building - and even reveals the original staircases and ceilings covered up by later occupants - to create a colonial atmosphere amid the ultra-modern fittings.
Sitting in the foyer bar, it's easy to imagine British officers confusedly downing one last glass of champagne, while in the bunker opposite poor General Percival was surrendering to the Japanese.
But that must have been a gloomy scene, so for my last evening in Singapore I abandoned the park for the city's hustle and bustle, sipped a Singapore sling and then surrendered to a delicious seafood banquet at the 62-year-old Longbeach Seafood Restaurant. It was superb.
I bet not even the 14th-century sultans ate as well as that.
CHECKLIST
Getting there: Singapore Airlines flies up to three times daily from New Zealand to Singapore and then beyond to destinations around the world.
Where to stay: Hotel Fort Canning is a modern hotel set in a tranquil historic park in the heart of downtown Singapore.
What to do: Visit Fort Canning Park.
Further information: See yoursingapore.com.
Jim Eagles visited Singapore with help from Singapore Airlines and the Singapore Tourism Board.
