Reverse lights are switched on via the PNP when the shift selector is moved to R, so that being the cause of no reverse is out of the mix. An issue in the remainder of that circuit (going to the TCM) is possible, but would be a real long shot. However, I do recall someone a while back posting that the TCM connector in their Aveo had become corroded, so that's something to check as well. My '05 is a standard, but IIRC, the TCM on my daughter's '06 is located next to the brake pedal assembly.