Most likely your steering wheel position sensor is out, going out, or has corrosion on it. Being that yours is a C5, I would go ahead jump on the corvette forum, and buy a steering wheel positioning sensor and change it out. You will be very thankful you have a C5 for this change! The sensor is only $50 or so from GM parts direct on the forum. To make sure this is the cause before you go and change it, check your codes. To do this, turn your key into the on position, and hold the #5 options button along with the #1 button. Once you've done this your codes should scroll thru across the bottom of the dash. The code you will probably find is the 1287 or 1288. These indicate the SWPS is having issues. Cheap repair and worth doing while running through a brake change so it stops bugging you! If it isn't that, it will be the ECBM, which is a different and much more costly deal. Absfixer.com will rebuild yours for $150, but you will be without it for a little while. Cost for a new is out of sight!
FWIW, I recently had to change mine, b/c it started acting up on me right after I changed tires. The SWPS pays close attention to camber, toe, and alignment in general. My father has a c6Z and recently had to change his right after a brake pad swap as well. The C6 SWPS is much much more costly!
Like I said, the SWPS pays close attention to all things suspension geometry wise. It is most like what is giving you the aggravation.