Your "Interior Lamp Delay Timer" has quit. The hatch release buttons in the doors aren't supposed to work unless the interior lights are on. This Delay module is located behind the passenger side "knee pad".
Replacement modules are available from several of the Corvette specialty catalog shops, or you can bypass the module by removing it, then installing a jumper wire between the two white wires at the module connector.
If you want to repair your module, I found that the module in my '84 needed a new Q1. I replaced Q1 with a 2N2222 transistor. Q1 is the transistor closest to pin E of the connector. Here's the schematic:
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