BMW brought it from its motorsport museum in Munich, specifically for the New Zealand Festival of Motor Racing, at Hampton Downs in January. The 3.0CSL is valued at $1.5 million.
Amon walked around it, chuckled at its four wide slick tyres, ran a hand over the bodywork and massive rear wing, opened the driver's door and settled down behind the steering wheel.
"I don't remember if this is the actual driver's seat from 1973 but it feels good," he said. Then he drove down memory lane, back to a year of touring car race rivals such as Jackie Stewart, Niki Lauda, James Hunt, Jacky Ickx, Jochen Mass, Jacques Berger and the crash deaths of drivers Rodger Dubos, Hans-Peter Joisten, and Massimo Larini at Spa.
Amon's race career from the early 1960s through to 1973 had been pretty much confined to Formula One and sports racers like the Ford GT40, Ferrari 330 P4, and McLaren Can Am cars, among others.
"I found the CSL touring car quite a handful after Formula One," he said. "There is more roll, more vertical movement. You are sitting a lot higher, not that that makes a lot of difference.
"But it took me a while to adapt to the car. You don't have the same degree of surplus of power in a touring car as you have in Formula One. You tend to overdrive them at first and you end up going slower."
Amon said his first drive in the CSL was at practice in Austria for the four-hour Salzburg race, the second event on the 1973 calendar after Monza. "Then it snowed so they cancelled the race. I can't remember doing a lot of testing after that."
Amon and Stuck missed the next race at Sweden's Mantorp Park but lined up for the fourth event and a win in the German six-hour at the Nurburgring.
CSLs finished one, two and three. Niki Lauda grabbed pole, set the fastest lap, and came in third. Dutchman Toine Hezemans, Austrian Dieter Quester, and German Harald Menzel took second place, eight seconds behind Amon and Stuck.
"I was still getting used to the car," said Amon. "Stuck was very good and the worst thing is to be slower than your teammate. The next [24-hour] race at Spa gave me the chance to have two- and three-hours stints at the wheel. Then I was sort of on the pace."
Stuck took pole position and Amon set the fastest lap, but the pair retired with engine damage. The Spa race was marred by the deaths of Frenchman Dubos, German Joisten, and Italian Larini.
Amon qualified first in the next event in Zandvoort, Netherlands, but he and Stuck retired after an accident. They had better luck in the seventh event at the Paul Ricard track in France. Amon set the fastest lap on the way to the team's third place.
The final four-hour race of the season was at Britain's Silverstone track. As usual the race was divided into heats of two hours each. Stuck took the drive but retired with clutch problems. He and Amon finished the 1973 championship with 32 points, equal-seventh with Lauda.
The BMW 3.0CSL would go on to dominate the European touring car championship, winning every year from 1975 to 1979.
* The January festival has a BMW theme. Organiser Jim Barclay said the 3.0CSL would be joined by cars like the JPS BMW 635CSi and JPS BMW M3, the ex-Peter Brock/Jim Richards BMW Mobil M3, and the ex-Denny Hulme B&H BMW M3. "We even have a DTM [German touring championship] car coming, which should wow the crowds all by itself," Barclay said.