Hi,
It's definitely a Singer red eye. I have a treadle model like it. The serial number will tell you the age of the machine. If you have a reputable sewing machine service person in your area, they can clean it inside, adjust any tension problems etc. I have a local dealer who once worked on a late 1800's treadle model!
I have info on how to restore the cabinet without stripping/restaining it etc. If you're interested let me know and I'll look for the info.
What a treasure to have an antique like this from within the family. Enjoy!
Roseann