It actually helped a LOT. I had been (unsuccessfully) searching combinations of "copper", "car", "lightweight"', "postwar" (judging from the general look of the illustration) and not finding too much. Your latest comments got me adding in "aluminum" and then "magnesium" and certain combinations started showing a few cars, but none of them remotely like the puzzle car. I noticed a few magazine illustrations from the Revere Copper & Brass Company so I threw that into the mix as well . . . And the combination of "Revere", "magnesium", and "car" finally led me to it.
It's an illustration of a lightweight car that appeared in the May 21, 1945 issue of Life magazine. Sponsored by the aforementioned Revere Copper & Brass Company, it was not actually a proposal from the sound of it, just an illustration of what a car made with high magnesium content might be like. This was a fun one, and I uncovered a lot of wacky "future lightweight car" proposals along the way. Hope I can remember them all!