should hear the pump run in the vette, unless you have the jukebox set at full volume, or the batteries are dead in your hearing aid.
pump diaphram failures are very common, less often the bladders harden and disintegrate in hot environments (''southern'' cars are most affected, but ''northern'' cars that sit in the hot summer sun with windows up get fried too) --if you find little cloudy chunks of plastic on the carpet behind your seats, that was the bladder.
if you hear the pump ''click'' but not buzz, it's diaphram time...cut a 1-1/4 inch o/d circle with a 1/8inch hole in the center from the smooth upper cuff of a good quality latex dishwashing glove (seems like the ''yellow'' ones are best) and install it in place of what was left of the original...nothing critical here, just observe how things come apart, reverse procedure to reassemble...and the ''latex glove'' diaphrams last much, much longer than oem ones.