My personal opinion is they were all "supposed" to have them Joop, and although it is indeed possible one slipped out the door without it, I would think that it would be highly unlikely. Regarding your car, ...my thoughts are "why" did it get a paint job in the 1940's? The simple answer is probably 'Because it needed one'. The reason it needed one is usually from being washed and/or polished so much that the paint wore through. The pinstripe would have been easy to polish off too, especially if an abrasive cleaner or polish was used with any frequency, --which did happen often.
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