Just to start, you do not need to use a larger wire. The larger wire only carries more current and that is not necessary for this system so just stick with the same size wire or at least close but no smaller.
Next when you removed the wires from the immobilizer, was the battery disconnected? If not then the vehicle thinks it is being stolen and shuts down the vehicle.
Here is a guide that helps with resetting the system:
https://www.2carpros.com/articles/how-to-reset-a-security-system
Below is the process from the manual that will help with replacing the steering column.
Please run through this material and let us know if you have other questions. Thanks
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Sunday, June 27th, 2021 AT 8:28 AM