Third-second-first is the mantra I repeat as I wait for the signal to fire up the Jaguar XJ13. I’ve never even sat in it before, and here I am about to drive it up the Goodwood hill in front of tens of thousands of people.

I can now tell you that the XJ13 isn’t an especially difficult car to drive at demonstration speeds, as 1960s race cars go, but I didn’t know that as I was waiting for the off.

All I knew – other than the vital figures of quad cam 5-litre mid-engined V12 with 502bhp at 7500rpm (and a redline of 8500rpm), designed for Le Mans (but never raced) and later crashed heavily in testing at MIRA by Norman Dewis – was that the gearshift can be really tricky, and the only chance of finding first when stationary is to go from third to second to first, and very gently at that.

So what happens to drivers at the Festival of Speed? Queuing, basically. First you wait in the paddock. Then there’s a flurry of activity when the marshals say it’s time to go, and engines are fired up. Fuel pump switch down, ignition switch down, and then pushed a bit further to operate the starter. A bit of gas and – whoomp! – the V12 roars into life inches behind the cockpit. Yee-haa!

Clutch down (it’s surprisingly light), third-second… Nope. Try again. Third-second. Oh hell, the other cars are moving. Third… The harder you try, the more the long linkage to the rear-mounted gearbox fights back. Gently now, third-second-first. Yes! Carefully up with the racing clutch, don’t really want to run over the crowds gathering, and I join the end of the queue of historic Jaguars in Group 5.

Half an hour of queuing follows. The Vulcan flys over and we all gawp at that, then look round and the front of the queue is moving rapidly towards the startline. Crash helmet and goggles on, engine fired up, third-second-first, got it! Nerves are gone, strangely, and minutes later the marshals wave the flag.

Stalling the XJ13 on the line would be very embarrassing but with about 2500-3000rpm and judious use of the clutch I make a smooth and reasonably quick getaway. It accelerates hard, this lithe alloy-bodied creation, and nipping it into second gear sees it pulling hard towards the first corner.

Off the gas a bit, not wanting to pootle round like a girl (with apologies to the many, many girls who’d be faster than me) and certainly not wanting to have a ‘moment’ in front of the Jaguar VIP area. Into the second corner, which is much sharper and tighter than it looks, and a quick blast past the house and under the bridge, ever conscious of the notorious Molecomb corner that catches out so many drivers.

It’s blind, the approach to Molecomb, and easily misjudged, and I’m driving a unique car that’s worth an estimated ￡10 million or more. And I’m not a proper racing driver. The desire to show off put firmly aside, I back off early and cruise round Molecomb before giving it a mild dose of beans past the next set of grandstands then taking it very gently indeed past the flint wall and through the following corners. I’m suddenly more conscious of how fantastic the engine sounds, even well below the Jaguar-imposed limit of 7000rpm, and the last blast to the finish line is the most enjoyable yet.

There’s a surprisingly large crowd watching over the holding area at the top of the hill, where famous drivers mingle with over-excited fools like me. A few more minutes of waiting and off we go again, back down the hill, trying not to let the XJ coast in gear because the mechanical fuel injection keeps pumping fuel in and tends to foul the plugs. It’s only on the way down that you notice just how big the crowds are, and how enthusiastic the marshals are, waving and grinning.

Back in the paddock I can’t find reverse, but this brief moment of further ignominy is nothing to the buzz of having driven one of the world’s most famous cars up the hill at the world’s greatest car show. The Jaguar Heritage guys laugh at the width of my grin – all I can do is thank them and eventually slope off to practice my best ‘it was this big’ stories.