Well this is a tricky one, but I have an idea here, with a way to test it.
Now inside of that control box is tricky, and if you are not extremely handy, I would not open it up. If you do, and you can not get it back together, it is not something I can tell you how to do over the internet.
The tick could be nothing more than a piece of broken plastic rattleing around in there.
Or, if it sounds like the AM radio like you stated, can be this, and this is what i'm thinking.
Inside of the control box, attached to the keyswitch, is a kill circuit wire. The way the ignition system works is that it supplys 100+ volts to the CDI box. That 100+ volts also runs up a wire and into the keyswitch. Now when the engine is running, there is that 100 volts on that wire, but it does not go anywhere. When you turn the keyswitch off, that 100 volts goes straight to ground, and does not supply the ignition system with power anymore, and the engine turns off.
Now on that wire that 100+ volts comes down in pulses. If the wire for it was chaffed against the alarm, the ignition system should cut out, and you would not get wide open throttle. But what i'm thinking is that the alarm is on its way out, and the voltage is ghosting its way into the alarm circuits via induction, and the little speaker in the alarm is reacting to the magnetic fields on the kill wire when it should not be.
The easiest way to test it would be to disconnect the black wire with a yellow strip at the powerpack on the engine and try it out. If the tick goes away, that is the problem.
Couple of items to read;
Let me know if that solves it or not.
Post back here with any additional questions or concerns my friend.
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