Dear royce1-- The problem you are having with your 1985 Chevrolet Corvette is indeed probably due to a faulty sending unit, located in the fuel tank. Go to the following site to see if you are experienced ( and patient) enough to do the repair job yourself-- http://autozone.com/az/cds/en_us/0900823d/80/21/96/f3/0900823d802196f3/repairInfoPages.htm. Good luck from Bovan.
It was indeed the sending unit; we went ahead and replaced the entire fuel pump with the sending unit attached to it. Works like new! Thanks for the advice.
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