1989 - 1990 Corvette: Howling, or Squealing Sound Coming From Clutch
From Jim Ingle, GM Powertrain Engineer:
"The problem you're most likely experiencing is a noisy crankshaft pilot bushing. There is a later design released for service that tends to retain grease better than the one you have and therefore doesn't squeal when cold. Unfortunately, the transmission has to be removed to access the bushing, so it's not a minor repair although the part cost itself is trivial.
In the event you're not familiar with these parts, the input shaft to the transmission is externally splined to connect to the inside spline of the clutch disk. The forward tip of the transmission shaft is a smooth section that is located radially by the bushing in the end of the crankshaft. When the clutch is engaged (foot off the pedal) the transmission input shaft turns with the crankshaft, so there's no relative motion. However, when the clutch is released (foot on the pedal) such as when you're at a traffic light, the transmission shaft is not turning and the crankshaft is. This is when the squeal would occur with a dry bushing.
The new bushing has grooves in it to help it retain grease and it seems to have solved the problem."