If you can provide even an rough estimate, it would be appreciated.

On eBay at the moment, many Masonic watches for sale of all styles and vintages. I see one for sale searching 'waltham masonic watch' and bidding is at $51 with a day to go. I don't know how many were made, but I think the Waltham Watch Co has a museum and probably a website.

Thank you for the effort, mint condition watches go around 1000 dollars. The number of produced watches is what I'm looking for.

My apologies for info you didn't need and for being nice about it. I had eBay open at the moment and got curious, even though I figured you knew already.