A clicking sound could be that the internals of the speedo are defective. There is a set of gears that drive the speedo and the odometer of the cable connection and one of those could be bad or worn, hence the clicking. It's not a real hard job to remove the ccluster from the dash, but take it real slow and don't force anything. I would look in some of the Vette mags for a service that will repair speedos. Usaully in the ad sections of these mags there are a number of companies that will repair or replace your speedo and odo. Hope this will help you out.
Jim