Here's my 2 cent worth. I would say You have diagnosed the problem perfectly. The ICV is sticking open and the act of unpluging and repluging jolts it bact to working. If the amp was bad you would not help to unplug and plug. Next time try just taping ICV to see if it starts working.

The KE control unit (fuel computer) has very little to do with warm idle. The idle is controlled this way. The throttle valve closed, air goes thru a hole in the fuel mixture assembly thru the ICV thru the air distrbution tubing straight to the fuel injector holders. The amount of air the ICV allows thru determines the amount of deflection of the air metering plate, thus the amount of gas to injectors. If the ICV stuck open to much air to much gas to much rmp.