My guess is that you're getting electrical noise into the circuit board of the receiver. What kind of unit did you purchase? Can you wrap it in tinfoil as a test, to keep out extraneous RF? The thicker the better, so you might want to fold it over a few times. Typical car antenna connectors are not UHF style, so I'm wondering what kind of connector the tuner has, and how you connected the antenna to it? This is a VERY important junction, and you're going to witness a dB loss, unless the receiver can accomodate the stock plug.
I'm just curious, what year/color is your Vette? I have a station wagon, but sometimes I pretend I'm in a Vette!