this might be a dumb question but............
If it's a C5:
http://wiki.answers.com/Q/How_do_you..._2001_Corvette
If you drive around for an extended period (or a week or two of normal driving) the socket will melt and you'll have to splice in a new one.
If you can't get around to changing the bulb, the only other option is to go into the big fuse box under the hood (by the battery) and pull fuse #2.
That will deactivate the daytime running lights while still allowing your signals to work. Keep in mind those same daytime running lights including a burnt out bulb will be on at night while using your headlights....
p.s. congrats on getting your 'Vette.

p.p.s. If you really have a mullet I'd like to see a picture.
On my car, what I do is, left or right side bulb goes out, I lay on the ground in front of the car, take the BRAKE duct(the black opening under the DRL/BLINKER LENSE).... and push that down,.... go ahead, it won't break. Push it down, and out of the way. You do not need to remove the duct at all.
Now, reach in,...yes, it is very very tight,...and hurts me every time I do it but, i'll gladly deal with it for a minute or so,...to save myself time ( jacking up my extremely low vette, removing the front wheel/loosing the screws on the front of the inner fender, and reaching it like that).
So, again, oush the brake duct down, stick your hand in there,...reach around, it should be very close,...grab the light,...press in the quick release, and turn counter clockwise, one half a turn. Pull the BLUB AND HARNESS OUT TOGETHER, do not undue the connector, untill you have the bulb and socket on plane site. Change your bulb, carefull, don't push the new one in too hard,...I had one break on me once,..and it hurts like a bitch.
The harder part, for me is putting the new on in, plugged in( I have tried it unplugged, it's worse). Once locked in,..pull the brake duct back up in place,...and your good to go.
I hope I explained that well enough.
Peace

