My wonderful Haynes manual says, in the how to check the ignition switch chapter "Trace the ignition wires to the wiring harness."

OK, I should have bought the Chiltons manual.

I'm not having luck tracing anything with a cursory look. Short of pulling panels, dashes, steering wheels, etc., then discovering it's under the hood, can anyone narrow it down for me?

'97 Rodeo, 3.2L

Symptoms include not starting for the first 111 tries, the radio suddenly decided to stay on, even tho the switch is in the off position and the keys are pulled.

Wow. Looks like I stumped everybody.

How about this one: How do I go about trouble shooting the switch and or the starter?

Well you can try to bypass the ignition switch completely and jump the terminals on the starter to start the vehicle. If it starts immediately and consistently then it is the switch. Otherwise, you might have a bad starter solenoid or sticking starter motor.