Glenn had a neat tutorial on fixing the finish and it won’t exactly work in your case. The oil won’t help your cause at all.
Cleaning and repairing the Shellac clear coat on Vintage sewing machine heads You will have to real add of this to find where he talks about machine with flaked off japanning. I don’t think Glen supports the tutorial these days. I believe he uses something to cover the bare spots. That machine will never be restored enough to be in original condition. You might consider painting. I had one that was so bad I just scraped most of it off. It looked kind of cool that way so I shellacked right over it. It made a smooth surface and was a functional machine once everything was cleaned up.
Beauty IS in the eye of the beholder Here is the crusty old think I just shellacked. And you can’t tell much. It’s the first pic.