I believe a '71 is still a mechanical oil gauge.  However, mechanical gauges
do go bad with age and it is 35 years old.

1. What is the pressure cold, or when you first start up?

2. Does it drop from the cold pressure to the hot pressure?

3. What weight oil are you running? Dino or synthetic?

Get another mechanical gauge, preferably one you know is good. Go buy a
cheap oil gauge at AutoZone, Pep Boys, whatever and hook it up.  The oil
connection is on the back of the block near the distributor on a small block
and on the lower left side by the oil filter on a big block.  Then see if
the pressure is the same.

If it really is zero, it is time for a new oil pump.  Do not buy a high
volume, high pressure pump.  It really isn't needed and wastes horsepower.

It is relatively easy to change on an old Corvette.

Turn the front wheels to the right.

Disconnect the ilder arm on the tie rod from the frame.

Turn the wheels slightly left while someone pulls down on the tie rod. The
idea is to get it to drop v-shaped much lower than the engine.

Drain the oil and remove the filter.

Remove the oil pan.

Remove the oil pump at the rear of the engine.

Remove the screened pickup tube from the old pump.

Install the pickup on the new pump.  If loose, use safety wire to tie it on
or drill a VERY small hole in the pump and tube to pin it. Small meaning
like 1/6 or less.

Install the pump.

Install the pan with a new gasket.

Turn the wheels and reinstall the idler arm.