[/quote]
I wonder if you've got a 9 volt coil and, as Arwyn suggests above, someone's removed the ballast resistor in the past leading to 12 volts going permanently through a 9 volt coil and the coil overheating. This could explain why the car fires when it cools down.
If it's a Lucas coil it should have something stamped on the bottom. [/quote]
With the wonders of a smartphone to hand I've been able to read the numbers on the bottom of the coil - BN-16 HPC 101 12V - but as they predate the internet age by about 30 years not surprisingly a search doesn't bring up an ebay listing! However Melvyn R is on the case.