Here's another "accidental" eBay purchase to share with you. Originally I assumed it was the same firm but now I'm not so sure. This William McCulloch having his firm in Maybole, South Ayrshire, Scotland. I do love it and wonder if there can be many others like it given it was probably used like a business card or advertising flyer. Any information greatly received especially if this is the same McCulloch from "Wales & McCulloch" in London.
Edit: June 2023
I found more examples of this item, apparently they are "service discs" which I'm assuming would be included when you had your watch serviced.