If you can see this picture, it is from a Google search. Gramma's watch is exactly the same except her dial has a lot of bubbling under the paint near the top.
I can see the photo from the Google search, but it's not very clear, so I can't work out if the logo above the 6 o'clock marker is a Daini logo or not. That probably wouldn't help narrow down the age anyway, since I think the Daini and Suwa logos were already being used by 1969, and were still being used in 1979 - I think it was used from around 1967 to around 1992, or perhaps a few years later. Interestingly, when I search for the model number 11-3649, I get photos of different watches to the one that you show. The "9" at the end of the case number means that the watch was made for the North American market, as opposed to "0" for the Japanese Domestic and some other international markets. The manual-winding calibre 11 was made fairly late - Ranfft says it was produced in about 1965: www.ranfft.de/cgi-bin/bidfun-db.cgi?10&ranfft&&2uswk&Seiko_11A