’04 Sienna Transponder Bypass

Hello, I have installed a remote starter on my 2004 Sienna AWD. All is well with the exception of the transponder bypass. Does anyone have advice on how to wrap the wire around the key cylinder? The transponder coil is just beneath the portion of the illiminated ring that barely fits within the steering column shroud. Even with 5 loops of wire I can not get the immobilizer system to recognize the key.

The system will remote start with a key insterted into the ignition.

I suspect this is an RF problem, and there must be a trick to # turns and where to wrap them.

I am using the TBKIII bypass kit.

Thanks for your help!