Production of the Cabriolet was relatively limited due to the depression and them being among the higher priced model A types. It is likely that most of them were made at the Mack Avenue Briggs plant where the Lebarron Studios were housed at the time. They designed the and built the first Briggs Fordor bodies and Ford's open car bodies of which the only two I know of were the 68 series Cabriolet and 180-A Deluxe Phaeton since Ford and Budd built most of the other open car bodies
Another tidbit was the way those first indented firewalls were made. Evidently they had a lot of flat firewalls left over when the new fuel tanks came on line. They reformed a lot of the firewalls for the teardrop indentation so they could stay in production. This is a link to Vince's site with a photo close to the top of the page.
https://www.fordgarage.com/pages/US2831bodystyles.htm