If you switch on the ignition and wait 10 seconds, does the clicking stop? Then possibly what you hear is the idle control valve and/or amal valve.
You can test this by disconnecting the wiring from both and turn ignition on again. No sound or do you still here clicking?
My guess: the electrical part of the ignition switch is defective.

On top of the starter motor is the start-relay. It has a big 12 volt connection for the starter motor and a normal wire. This wire should have 12 volt on it when you turn the ignition switch. Can you measure what happens at this wire?