The plug on the alternator is convenient, but spade terminals on the ends of wires will connect them to the blades on the alternator. You'll have to remember which wire goes where, and it's probably not going to hold them on as secure as a new plug, but it'll fix the immediate issue and kinda blend in with what's under the dash (sorry, couldn't help that)....
(I'd also like a new plug if you find a source, cause trying to remember which wire goes where with spade terminals challenges my short attention span)
If the wires are too short, you could butt splice them with longer wires, but they should only go back to the regulator, on the driver's side firewall usually I think, under the master brake cylinder. Shouldn't be difficult to run two new wires...
But, these should go from the Alternator to the regulator. I'm really not sure how they'd blow any fuses.
The rest of it... You could just pull it all. Read some threads from people that have done this for tips first. I think it's
@Coolerman I've heard rebuilds these for people and has been open about sharing methods. Label everything, take pictures, etc.
short of that, start pulling out wires that aren't connected to anything. Cut any ties you need to. If wires run into original Toyota harness, I'd be cautious about cutting into it without taking it out of the vehicle and totally cleaning it. You should be able to find out what for and where they go on the wiring diagram, and if unused cover with shrink tape to make sure they don't short. (unless you're going to totally rewire it).
Then start replacing wires with wire nuts, replace with but splices or whole new wires.