Hi - I am quite sure your fiat is a 503 - the 501 had quite a different radiator and bonnet shape.
The 503 was technically built from 1926, and was based on the 501 mechanicals, but I think it also had front brakes (as per the 501 last models)
Given the oral history about it being a show car, perhaps this was an early build for marketing, hence the 1925 build date.
Parts for these are most available in Australia, NZ and Sweden - I think because they tended not to be scrapped for the WWII effort.
There were a number of OHV models made - these were the S models, and gave a top speed of over 65mph - if you have an OHV engine, it will be very rare indeed.
Do you need any parts?
Cheers
Alex