. 3.1 engine, auto trans. A/C.
When I turn the ignition key on to start the car the fuel gauge needle jumps to about the 1/4 tank fill mark, then drops back to the empty position.

Any suggestions please?

Welcome to AF

The fuel level sensor has probably failed. It's a variable resistor attached to a float, and is probably shorted out causing your guage to be inoperative.

My wife's car does the same thing. She has the same car as you do. I have heard that these cars fuel level sending units are prone to failure and are very expensive. We fill up every 300 miles.

The AC-Delco part number is SK1090 (GM#25323812) and runs $178 dealer retail. You could get it significantly cheaper at an AC-Delco authorized parts store if you have one in your area.