The rear window, which had worked perfectly, suddenly cannot be controlled from the dash switch. The window still works properly when controlled using the key in the hatch.

Hello,

I had the same problem on a 91 4runner. I am not sure about the 05 model, is it lift-gate or tailgate?
The 01 was tailgate, the problem turned out to be that a couple of wires in the wire harness between rear quarter panel and the tailgate broke and lost connection to the panel switches. The reason the key works is because in these trucks the rear window is energized all the time and the key and the panel switches close the circuit by connecting to ground.

If you have a lift-gate you should be able to see the wire harness at the top of the gate. If you have a tailgate you will find the wire harness underneath the tailgate on the left (driver's) side of the truck. it goes between the tailgate an the inside of the rear quarter panel.

It is not hard to fix but takes time to find the wires, unless you find a service book with the wiring diagrams.