There are a number of wiring diagrams on the 'net for Singer and other sewing machine motors. I've got a bunch of them on my hard drive, but I can't post them cos the forum considers them as being copyrighted. You'll need to do a search of net, they are there. I'd post the links, but those I lost with the last HD that died.
In lieu of a wiring diagram, you can carefully mark the old wires and install the new ones in exactly the same position and routing.
Joe