The television presenter and historian is keeping tight lipped at the moment. He has spent close to two years attempting to solve one of Scotland's enduring historical mysteries and a debate that has raged for centuries: the precise location of where King Robert the Bruce and his army conquered the English forces.
Oliver's journey will be charted in a two-part BBC Scotland documentary, The Quest For Bannockburn, to be screened next month marking the 700th anniversary. For now, though, I'm having to be content with knowing that where we stand is somewhere in the general vicinity.
Half an hour earlier we had embarked upon a magical mystery tour. Leaving Stirling, rows of shops and leafy streets slip past the car windows in a blur, the newly opened state-of-the-art Battle of Bannockburn visitor centre following suit. Finally we reach our destination: a non-descript suburban housing estate.
Exiting the car, Oliver strides ahead as the rest of us - the photographer, Oliver's publicist and myself - scurry behind him along a narrow pathway. We look like the Famous Five minus Timmy the Dog in search of adventure. I wish I'd remembered to pack some hard-boiled eggs, jars of potted meat and ginger pop.
Traversing the banks of the fast-flowing waters of the Bannock Burn, we pass under a graffitied bridge and on to soggy farmland, strewn with wind flattened grass and cow pats. The A91 is only a stone's throw away, the hubbub of passing cars competing with the occasional thundering roar of a train on a nearby railway line.
Part of an area of low flatland, nearly 60 square miles, known as the Carse, it is one of eight sites - including bogs, high areas, woods and even back gardens - which have been scrutinised as part of a massive archaeological effort spanning two years.
I examine the ground beneath my feet for clues to it being the possible location of one of the most famous victories in Scottish history. Alas there is nothing which gives it away.
Earlier in a Stirling tearoom, Oliver had spoken of his long-standing curiosity and fascination with Bannockburn. Alongside good friend and fellow archaeologist Dr Tony Pollard, he first set out to uncover its location for the BBC television series Two Men In A Trench in 2004. He admits on that occasion they "found precious little - almost nothing" to prove its whereabouts.
"You are chasing ghosts," he says. "It's difficult. Seven hundred years is out there at the point where nothing survives. Even if you are standing in exactly the right place there might be nothing to see because it's gone. It's not that you can't find it, it's just it is no longer there."
Yet undaunted, two years ago they returned for a second crack. The project, fronted by Oliver and Pollard, has seen BBC Scotland work in tandem with Glasgow University, the National Trust for Scotland, Guard Archaeology, Historic Scotland and Stirling Council.
It involved more than 1150 people including a core group of six professional archaeologists and five of Pollard's students from the Centre for Battlefield Archaeology at Glasgow University, as well as more than 360 adult volunteers, 740 schoolchildren and 50 metal detectorists.
"The big debate has always been whether the battle was fought down in the Carse or an area known on Ordnance Survey maps as the 'dry field,'" says Oliver. "Some people have imagined that the fighting would have taken place on the 'dry field' for obvious reasons because it was dry underfoot.
"The question was that if it was on the Carse, why would the English army have wandered down and made camp in a bog? For them to be stuck in a bog would seem to suggest that they had knowingly walked into one. We were always a bit sceptical about that suggestion.
"So, we did the environmental study and also the excavation has demonstrated that the Carse was dry." He pauses, catching himself. "I'm giving away results here."
Oliver smiles, choosing his words carefully before continuing. "Once and for all, after 700 years, is it possible to pinpoint the battlefield of Bannockburn?" he says. "As archeologists we can put our hands on our hearts and say we have done everything that could be done."
That has included attempting to make sense of conflicting and confusing accounts of what unfolded in the days leading up to and after June 23 and 24, 1314, when King Edward II and his English army attempted to relieve Stirling Castle. "If you look at the historical sources, they are relatively few," says Oliver. "Nothing was written down about Bannockburn at the time. There are four main sources but all were written at least decades after the battle. Only one of them is anything like an eyewitness account.
"That was written by an English knight taken prisoner by the Scots. Years later he wrote an account of what he had seen but it was for a Scottish audience to whom Bannockburn meant something different than it did to the English establishment."
The few geographic nuggets contained in such writings have proven equally vague and misleading. "They don't use place names that are still in use," he says. "Some of them talk about 'wet and foul marshes', others talk about 'a great gorge' and 'up on the dry ground'.
"It's tantalising but that's in the nature of war. No two people who witness a large-scale battle will see the same thing. It depends where you are, what you experience, what the ground under your feet was like. When you turn to run, do you run across a field or have to swim a river? The same thing isn't going to happen for any two people."
Oliver, 47, who lives in Stirling with wife Trudi and their three children, has previously presented Coast, Vikings and most recently Sacred Wonders Of Britain. Among the biggest challenges in his search for Bannockburn, he says, was managing the huge burden of expectation which came from the emotional investment many Scots have in the battle which inspired the lyrics of Flower Of Scotland.
"Everyone is looking for you to find Robert the Bruce's codpiece or a gold embossed sword with the initials 'RTB' on it," he says. "There is the belief that if you deploy a lot of people and metal detectors that you are going to find something.
"Television has its own completely understandable agenda: it wants results and to entertain. It's like those programmes when they say 'we're going in search of the yeti.' You know before you start watching it that obviously they didn't find it - because if they had I would have read about it - and with this it was that kind of feeling.
"You are trying to explain that after seven days, never mind 700 years, there would have been little left to find on the field at Bannockburn," he adds. "There would have been dead bodies for sure, shallow graves, and a few bits and pieces of broken armament but everything of value and significance would have been taken away within days.
"Then 700 years later - after corrosion, rust and the passage of time - we know going in that, if we find anything at all, you would probably be able to fit it on the surface of this table if not in that cup. We might catch a glimpse of Bannockburn - and it will be evocative and possibly thrilling - but probably not what you would expect."
It is his belief that Bannockburn is "almost a poisoned chalice" in some respects. "What it is remembered for, to some extent, it never was - not even at the moment when it happened," he says. "It was spectacular victory on the battlefield without a doubt, a completely unexpected reversal of fortune. It came out of a clear blue sky. Robert the Bruce was able to react and secure this luminous victory."
However, ultimately, says Oliver, Bannockburn was just another battle and it is only with hindsight that we have been able to attach this huge significance to the two-day event. "It didn't end anything," he clarifies. "England and the Pope didn't suddenly turn around and say: 'Scotland is an independent country and you, Robert the Bruce, are its king.'
"It was a stage in a process and it wasn't until many years later that there was any kind of acknowledgement of Scotland as an independent country and Robert the Bruce as king. Shortly thereafter the trouble started all over again. It didn't end or decide anything except the fate of the 20,000 or 30,000 people who were there that day."
Yet that, adds Oliver, doesn't diminish what a colossal accomplishment it was for the 9000 or so Scots as they secured a victory over an army that wasn't only more than twice its size but viewed as one of the most effective fighting forces in all of the world.
"Word of the defeat of the English by the Scottish army would have spread like wildfire," he says. "It was like a third division football team beating Manchester United in an unexpected cup final - but 100 times bigger than that."
The significance of the anniversary coinciding with another pivotal moment in our history - the Scottish independence referendum on September 18 - isn't lost on Oliver. "There is quite a lot of wry, almost with a glint in the eye stuff, because people are wise enough to know it's no coincidence that the referendum and the anniversary of Bannockburn have somehow come together as one," he says.
Oliver has previously warned against Scots "sleepwalking" into independence and said he believed people needed to have a "historical grasp" of Britain to make an informed decision. He says: "The analogy I would make is that we have been married to the UK for a long time and now we are basically saying: 'I feel like a change. I'm not necessarily going to move out of the house but I want my own bit of the house. I would like to continue to share the bank account. I want a share of the pension. I just don't love you the way I used to.'
"We've put that out there. So, no matter what happens as a result of the referendum, whether Scots vote to stay in the Union or not, it's already out there. If a wife had said to her husband: 'I'm thinking about leaving you, I'll tell you in six months time.' Then six months down the line said: 'I think I'll stay with you.' The relationship is never going to be the same again.
"I'm proud of Britain. I find this kind of internecine squabbling puts my teeth on edge. I would rather that it would just go away - or that it had never happened."
Some people might be surprised to hear him air these views given he is seen as so quintessentially Scottish, I muse. "I'm a proud Scot," he interjects. "It doesn't have anything to do with that. I like the status quo. Alex Salmond? The whole thing makes me think of the television series Citizen Smith with Robert Lindsay.
"Citizen Smith was a young Marxist. It was always 'freedom for Tooting'. It was the Tooting Popular Front he represented and he wanted wholesale revolution. He would steal tanks and drive them to Downing Street. Ultimately he was living a relatively comfortable lower middle-class life and wanted to rebel. You'd think: 'What is the revolution about? What is so bad? It's not as if you are coming out of the slums or an oppressed, downtrodden society.'"
Back out in the field on the outskirts of Stirling - Oliver is aware that whatever your sense of attachment to Bannockburn, the notion of finding a definitive location will attract interest. "You have got strongly entrenched positions," he says. "There are people to whom it's holy ground. It's a bit like if, in 1000 years' time, the Rangers faithful want to know where Ibrox was.
"People want to know where it is so they can go there, hold their son's hand, talk about Robert the Bruce, the Black Douglas and all that happened that day. It matters to them to know exactly where it was."
As for whether that mystery has been finally resolved, Oliver offers crumbs of hope. "There are scientifically backed-up, research-led conclusions that have come out of the project that should and will satisfy most of the academic and historic community about where the Battle of Bannockburn was fought," he says.
"Where it was fought is now beyond doubt - we know where that is. By the end we'll be pretty much standing on a soap box saying: 'We know where the Battle of Bannockburn was fought' and can point at it." n
The Quest For Bannockburn begins on BBC Two at 9pm on June 2.