There is a lot of information on identifying Singers - it's the other mfg that get confusing, as often they deliberately copied each other, and used similar names to "fool" buyers, or it was a badged name owned by the reseller, and the reseller switched suppliers a few times.
And then there was a lot of consolidation over time, and one company bought out another and continued to use the name for the brand recognition already established.
For US machines pre Japanese clone era, I've found that identifying what the attachment points/shuttle and needle goes a long way to identifying the machine. The shape of the needle plate is often unique too, or limited to only a few MFG, so it narrows down.
For leaf tension (top tension) I have also seen quite a bit of uniformity - also I don't think Singer ever made a machine with a leaf tension.
I am going to put together a chart that shows all this. I'll also be taking detailed measurements of round bobbins, and even experimenting by trying to use similar sizes in different machines.