I found it! I am so glad I took pictures of this machine when my student brought it to class last year! The Singer Touch and Sew was introduced in 1965. You can look at a 1970 version of the Golden Touch and Sew Delux Zig Sag Sewing Machine Model 750 sewing manual here (love the internet for finding things like this!) The graphics are super cool and it clearly shows the bobbin winding feature on page 7.
While researching this I discovered the google timeline and found several classified adds from the 1960s and 70s showing that this machine originally retailed for around $300. Not much has changed in fourty years!