‘88 White GMC - Fuel Gauge Empty When Key On, Works When Key Off?

That is not common. In 88 did they not still have individual gauges not the intergrated board? How long have you had it and what has been done to it lately? Sounds like some wires are crossed up.
I have wiring diagrams for some of those but I thank they are newer than yours.
Need more info and or pictures.

 

Jumping wires can become expensive! You are probably safe so far. Sounds like your gauge is OK and at least the sensor wire to the tank has a good circuit.
Those are good old fashioned independent gauges. The extra wires on the gauge is where they used the stud as a junction for other things. As to supply power to other gauges.
If you connect the two wires on the fuel tank to an old fashioned test light what does the gauge read? I thank you are looking for about a 1/2 tank but some brand trucks registered different. Thank you are still looking or 1/4 through 3/4 in any brand.
Can you run your arm in with the fuel cap removed and reach the float? What does it read when moved. You way have to take the sender out in order to test it but it sounds like a bad sender.

 

Of what I know about those gauges there are generally three wires that run them.

One is the power wire when the key is turned on, one is a ground wire, and the other is from the sender.

Just as a basic check, I would check the power wire to see if it energizes when you turn the key switch on.

Once you know which one is the power wire you can put your own 12 volts to it if you need to and see if the gauge works.

Also the two wires at the sending unit, one of them should be ground and one of them should run up to the gauge. Make sure your power wires are correct and your ground wires are correct and grounded properly.

@BoxCarKidd gave very good advice.