After seeing your latest photos, I would say that the black wire is used to stop the engine running, since it looks like it is connected to the HTIgnition coil. To stop the engine, the black wire needs to be shorted to ground. While the engine is running, the black wire should be open circuit.
The red wire is likely the battery charging supply as shown in the wiring diagram from the page you supplied. I would suggest you test the output from this with a voltmeter before you connect it to anything. If the wiring diagram is correct, there may be a diode in the connector. If this is correct, it will want to connect to the battery positive terminal, which will also be available on the starter solenoid.
