I will not go into details for fear of ruffling feathers (on the outside chance the owner would read this) but I know of a GM A body convertible in southern Manitoba that has a similar issue. The owner contacted me prior to buying the car to ask for help documenting it. When he gave me the VIN, it was not even for a convertible but for a same year hardtop car. I told him to run! In spite of that, he bought the car, has it registered and is driving it every summer. I can hardly believe that it passed a screening at the insurance desk.
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1966 Strato Chief 2 door, 427 4 speed, 45,000 original miles
1966 Grande Parisienne, 396 1 of 23 factory air cars
It would be worth getting the serial number off of the dashboard and buying a seller's kit for it just to see what the deal is. When I got the sellers kit for my '61 GMC pickup truck, it only listed owners back to 1980 but when I got the one for my convertible when I bought it back, it went back further than 1979 when I owned it. That being said, with this car, it might at least have owners listed back to when it was ten years old and then a person would have some idea of who had it and when and then be able to find out who it was last registered to and if it's this guy, then it should be safe; if it's someone else, I think I'd pass. Just my thoughts anyways guys.