Good Housekeeper machines are Japanese made. Good Housekeeper is not a manufacturer, but a name it was sold under. Often, a vintage Japanese machine was sold under several names. Sometimes you can get a manual from one of the vintage Japanese sewing machine groups on Yahoo. You would have to join the group to access their files, though.
You can Google for a Good housekeeper 850 sewing machine manual and might be able to find one.
Otherwise, you have to do is find a identical looking machine. Generally, they have a generic manual that just says "Deluxe Zig-zag" or something like that. I would use Google and Pinterest to find the machine under another name/names. Then, see if you can find a manual for that machine. You can also look at the sewing machine manual sites like
https://www.tias.com/vintage-sewing/machines/manuals/. Look at the pictures of the machines until you find one that matches.
I just did a search and someone said Good Housekeeper was made by White. So I would start lookign for a White 850.
Bkay