I did a search and some reading on this, most others fuel gauges either work or didn't work. It was a wire or sending unit.
My '68 GTO runs out of fuel at about 1/8 of a tank showing, ask me how i know, go ahead, i'll wait.
When I fill it up the orange needle can't be seen until about 6 gallons has been used.
It was reading above half and I put in 13 gallons in last night, with a 20 gallon tank it should have been below half.
Any one have trouble shooting info?
Does not sound like a problem to me. This is not a "modern" car. I can't think of when any of the old gas gauges were that accurate. The tanks are wide and flat, so I don't think you can get as accurate a reading like you do with today's gas tanks which are typically smaller, more compact, and located differently.
You could install a new tank sender, gauge, wiring, etc., but you may still have the same results. Don't let the gauge hit 1/8 as 1/8 may actually not be bone dry "empty," but at the point where the pick-up tube in the gas tank won't be immersed in the remaining gas. This may also account for why when you added 13 gallons, the gauge was over half because you still had 2-3 gallons in the tank that can't be picked up.
I have a '73 Fury that will show full when it is full, but use up a couple gallons and the gauge drops fast, but I know I have more than the gauge says. These old type set-ups can drop real fast from full to half, but then hang at half tank for some time. The gas can also slosh around because of its large size and you can watch the needle move around as you brake, accelerate, go up a hill, go down a hill, or corner hard. Nature of the beast - in my opinion.
It may be wiser to simply know how many miles a gallon the car gets and figure how far you can go on a full tank - when you fill it. Consider the 1/8 level on your gas gauge as your car's "empty" mark.