Not sure if this helps finding closure on this puzzle.
I have found information indicating that Mr. Eusebio Olvera built curved-dash Olds replicas in Cuernavaca Morelos, Mexico between 1968 and 1992. The replicas frequently use Briggs and Stratton engines. I haven't been able to find another source that confirms this information about the Olvera replica.
The puzzle photo, and another online photo I found of a claimed "1903 Olvera", include large padded arm rests for the front seats. I have yet to find a photo of an actual 1903 Olds, which shares these arm rests. Your average 1903 Olds has arm rests for the front seats, but they are made out of metal rods.