Suspect either an incomplete plug-in of the New Ignition Switch Module ... or perhaps the "Teeth" on the Switch have been "Mis-Timed". You could also have a
Sketchy Key-In-Tumbler situation inside with the Lock-Work becoming Worn Out.
If your Key Chain has been laden with Extra Keys that have been
acting like a Pendulum for years on end, this action of
constantly swinging back and forth on the Ignition Key can eventually wear down or loosen the Internal Lock Work Mechanism.
As a result of all this internal wear, if an electrical contact with the Anti-Theft System is momentarily broken as you drive, it can trigger the Disabling or No Start event to occur.
If your Internal Tumbler and Lock Mechanism is Badly Worn, you can purchase a complete replacement set with a New, Unique Key for the Ignition. Follow THIS Video for replacing the Ignition
after Properly Timing The Switch:
...
and THIS Video will show you How to Re-Key your New Replacement Lock-Work to your Existing Manual Ignition Key(s):
Will you please elaborate on whatever it was (precisely) that you did in order to Disable your VATS?
Last but NOT Least, Eric "O" from SMA (South Main Auto) does SUCH a Good Job of going over the Ignition Switch Diagnostics using the Wiring Diagram for the Circuitry for a 2006 Chevrolet Silverado that Your Vehicle shares as well
and knowing this information might help with further Ignition Switch Diagnostics: