I think there's another source of the brown sticky nastiness.
In some of the Singer service manuals, you will see a preparation list - ie what the machine was supposed to go through before a customer ever saw it. One of the steps is to remove ALL traces of the anti-corrosion film that was put on the machine for shipping.
I suspect that a great many machines didn't have all of this removed, especially the ones with brown just in the crevasses but look otherwise quite clean and don't stink of nicotine when wet.