The 1st to 4th "Computer Assisted Gear Selection" (CAGS) was something that Chevy did to improve gas mileage so that they could avoid gas guzzler tax. When you have a warmed up car at less than X% throttle, the computer will force you to go from 1st to 4th within a certain RPM range. It uses a solenoid of some kind to do that. It can be defeated by taking the car above about 2500-2800 RPM before shifting, or disconnecting the solenoid. The problem with disconnecting then solenoid is that the computer does not see an event it expects to see, so a trouble code is set. The CAGS bypass kit that you can buy from most of the Corvette aftermarket catalogs contains a device that mimics the solenoid. The computer gets the input that it wants, so there is no trouble code. I would bet that most manual drivers do the bypass. It costs about $20, and you can install it yourself, as long as you can get the car up in the air far enough to get under it safely. MsSchroder did an excellent step by step post quite a while ago, but I think you could find the thread.
Congratulations on the Z06. I have a 200 Z06 myself. I just got back from a high speed blast myself. What a kick to drive!
