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First check the 3A cruise control fuse, LCD fuse, and the CLUSTER fuse. Check the vacuum hoses for leaks, splits, seated on nipples, etc. Many times the brake switch is out of adjustment, this switch is open circuit with the brake pedal depressed and on my 87 vette, the switch has a dark blue and a light blue (manual xmsn), grey/blk (auto xmsn) wires. Past these easy checks, you need the diagnosis table from the GM electrical diagnosis service manual, get one, its cheaper than 1/2 hour at the dealer!
Also, from now on it would be very helpful to state what year vette you are asking help for.
Gordon Killebrews 1984-1989 Digital Cluster book 29.95 is fantastic-it covers about everthing from diagrams to most common problems to testing to fixing.