I think you have it.
There's one wire at the factory thermal switch at the bottom of the right radiator. You can test the fan's operation by grounding. IIRC, remove the wire, then use a jumper to connect the switch's exposed connector to ground. The fan should turn on. So, now cut the stock wire somewhere and install a SPDT (on-on) switch. One switch position goes to ground (that's 'new wire #3') and makes the fan turn on manually. The other switch position is normal, stock operation.

Yes, there's a bit of extra wire but it's easy to keep tidy and put a switch in an accessible spot.