Two nominations - not very exotic, but definitely quirky:
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Austin A35 Pickup in the real world
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enigmatic Commer Express 4-door Estate in India. No obvious explanation for who/how.
Another which I can picture but not remember the details - it was a traditional Brit 50s thing (Jag? Bentley?) convertible with German/Austrian/Swiss body in a late 50s Swiss/Austrian colour film parked in traffic along an Alpine lane on a sunny summer day. Body might have been a name something like Spion - there was some chatter on the page about what/who until it was solved.