Welcome. Your machine is a FR model as indicated by the serial number. There were later models that had numbers, which were indicated by numbers before an "X" followed by other numbers and sometimes without an "X". However, the manuals that came with them did not have model numbers listed on the manuals, but were titled "Book 9" or something similar.
I'm guessing you may have gotten the date for your machine from
https://www.treadleon.net/WhiteSM/whites.html. When I was looking where to find manuals for your machine, I found that there are at least a couple different versions of Book 12. One is for electric version and the other was for a treadle, but both titled Book 12. Here a few links for manuals for the Family Rotary or ones that will work for it.
https://res.cloudinary.com/singer-se...-9-shuttle.pdf
http://needlebar.org/main/manuals/white/index.html
https://ismacs.net/white/manuals/whi...ual-book-6.pdf has a different stitch length than your machine.
https://ismacs.net/white/manuals/whi...al-book-10.pdf
Have fun sewing with it.
Janey - Neat people never make the exciting discoveries I do.
Not affiliated with off-site link(s)