William Talman or John Talman

William Talman, Architect, or John Talman, Antiquarian?: I am posting this photo of a painting in hopes of locating the current owner as well as confirming the identity.
Beginning back in the 1930s, one of the cousins traveled around the country (US) gathering information and documentation on the Turpin & Talman families. This photo was taken during that time, but the label identifying the owner has disappeared with time.
It is supposed to be a portrait of English architect William Talman (1650-1719). When comparing it to other confirmed images of William, there is something not right about the shape of the nose. I wonder if it might be a painting of his son, antiquarian and artist John Talman.
If anyone has any information, I would love to hear from you!