P0412 code 458

Have you replaced the purge valves? They're like $35 and there's two of them. Not terribly difficult to replace.

 

458 Engine Ticking Sound....

 

The reason that you get the code every 3 or 4 starts, is because after clearing the code, OBD looks at the valve function, and will trigger the light after 3 consecutive starts with a pending code.
It's good that you used the 2 way scanner to activate the air pump, so you've eliminated that as a possibility.
There's a few other things it could be.
The code is not the typical "Secondary air valve, Bank 1 (or bank 2)", it is something to do with a "switching circuit", so I'm wondering if it's the solenoid that opens, to allow vacuum to be applied to the secondary valve. I think it's located near the oil fill tank.

 

I'm pretty sure that you can trigger that solenoid with the 2 way scanner as well, but it may just be easier to take it off and apply 12v to the contacts while blowing through the air ports to see if applying the current opens the valve. (that's what I did to check it when I was diagnosing the secondary air valve code that I was getting). At the end, my problem just wound up being the secondary air valve itself (I have a write up on it on one of the DIY threads here)

 

Maybe you can put a vacuum pump on it with a tiny bit of vacuum (the way the engine would), then activate it and see if the pressure goes to 0