http://www.google.com/search?hl=en&q=corvette+clock+repair&btnG=Google+Search
and
http://www.clockwks.com/Corvettex.html

I'd second Bob's recommendation:
  http://www.clockwrks.com

Here are several more:
 http://corvetteclocks.com/
 http://www.corvettespecialtiesofmd.com/
 http://www.bobsspeedometer.com/bobs/

fix it yourself.    seems to me that this is a wind up clock that does so
via a small electric motor when the engine is running or
ignition is on.   Remove the clock from the dash, open the case    should be
a set of contacts ( that usually pit or corode)
clean them up with an old 'point file' ( since your car still uses pints in
the ignition I assume you use or know what they
are....  or  use  fine  emery paper      then   spray the whole clock out
with brake clearer ( non-residual type) to get
rid of old dirt laden oil and use  sewing machine or clock oil on the works
....   test, reasemble  and put back in the car

worth a try anyway   since you have to pull the clock to send for repair
anyway