How does the fuel gauge low gas warning light work, even when level is incorrect?
 

Gas gauge was stuck at half.
Yet, warning light illuminated.
Realized sender or gauge was stuck or faulty.

I removed sender and made sure it wasn't stuck.
It was not.
I cleaned 3 prongs on top of the sender unit with wire brush.
Gauge now correctly shows empty.

How does gauge show incorrect level, yet low gas warning light works?

the light is triggered by a contact on the sender, when the float is truly at the bottom the light turns on, the gauge is a resistive reading based on how high or low the float is, so some crud on the wire will make the gauge inaccurate, but most times, the light will always work

don't trust the gauge, trust the light.

On this older thread someone had a similar issue. It goes into pretty good detail on troubleshooting the sender and the rest of the system too.
https://forums.pelicanparts.com/porsche-911-technical-forum/847863-fuel-sender-fine-open-fuel-gauge-itself.html

-Matt

How much fuel remains in the tank when the light comes on? Mines come on a couple times on hills when I was low but generally fill before it gets there.

In my 88' I let the tank go down until the light came on. I wanted to change some lines. Drained the tank. Took out over four gallons. YMMV. Any way I figured that I had about 80 miles left until bingo.

Good info, thanks.
So, the light verifies sender is not stuck, but contacts need cleaning, since gauge is not accurate

Exact same symptoms here, the light is accurate, and yet the needle never goes below about 1/3 - so i just trust the light

On my '82 I drained the tank & serviced the screen/filter. After re-assembly, I added fuel incrementally until the light went out. Took about 2.5 gallons to extinguish the light. In my estimation, when the light comes on you've got about 40 miles, max., maybe less. YMMV.

Try cleaning the contacts are the sender and at the gauge.
The needle should get closer to E.

I love that someone tested that out.

It has been a long time since I read my owner's manual, but I think it mentioned a 2 gallon "reserve" when the light comes on. In the daytime, with sunglasses on seeing that light is almost impossible. At night no problem.

light
 

Yup, that's what I found.
Gerry