The sinny 3rd wire is the wire that goes to the charging light. Without the little bit of resistance from that light bulb your Anternator will not charge; you have to have it.
The next time you are at the junk yard grab a charging light bulb and the bulb holder.
If the Toyota already has a charging (idiot light) it may be possible to use the same wiring setup but you will need to find out how many amps the different bulbs will pull.
Or alternatively measure the ohms of each type of bulb.

As long as the other 2 wires were connected to the + wires that go to the battery you can hook them directly to the battery.
In a past thread I ask why there were 2 wires that went to the same place and the only answer I could get was a speculative; they used 2 wires so the would not have to use 1 large one.

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84 300D, 82 Volvo 244Gl Diesel