OK, it is a bit of a mess... LOL
What would you like to do? Do you want to do a full rewire, or just get it running and charging?
If you just need it running, start by tracing the existing wires. If any that are cut off are still connected on the other end, they need to be disconnected so they don't short out against anything. They can stay, just disconnect them for now.
The alternator wire going to the on/off switch, it needs to be removed.
Run a 10 gauge wire from the BAT terminal on back of the alternator to the battery cable side of the starter solenoid or contactor, which ever it has.
Get a harness plug that fits the side terminals of the alternator.
Connect the red harness wire (#2) to the BAT post on back of the alternator, doubled up under the 10 gauge wire you ran to the battery cable.
The white wire (#1) will go through the indicator lamp I mentioned above, to an ignition source, either the back of the ignition switch, or the wire that feeds the coil, which ever is easiest. The indicator light is simply being used as a resistor. If you want to have it visible as a charge indicator, you can put it through a hole in the dash, or somewhere visible. Or just tape up out of sight, it will serve the same purpose.
That should get it charging and you say it already runs and cranks, so as long as those circuits are intact it should be good to go.
When you get ready to rewire it, it will be easier to make your own wiring harness. If you buy one, it will come set up for a generator, and will have a lot of unused circuits.
You can do this, one wire at a time!
Harness Plug