Most likely you have no baffles in your tank. You can put a capacitor between the sender post and ground to damping the voltage changes seen by the gauge. Capacitors by design oppose changes in voltage. I’m a fan of electrolytics. I would first try a capacitor used for noise suppression. Others might know the exact size you need.
To reinforce beltfed's advise. If you have the OEM tank you likely had a baffle break loose. My '38 has all the baffles in place and it'll move 1/4 tank going around corners and up hills. My '53 isn't as bad but moves around some. It's easy to test your sending unit.
Save a life, adopt a senior shelter pet. The three main causes of blindness: Cataracts, Politics, Religion. Name your dog Naked so you can walk Naked in the park.
Hi Rick...It can mean your sending unit is wearing out, and this is common. The original sender unit wore out in a way which over time causes it to do exactly what you've mentioned. The body was pot metal and there was only one pivot hole for the float shaft (you can see this in the images attached). As this hole wears larger and more oval shaped, that causes the wiper to contact the rheostat coil more and more intermittently. This tendency is worse when your tank is between 1/2 full and full (or when you are close to empty)...because that wiper is at the bottom of the rheostat coil when you're full (top when you're nearly empty) and it can move around more in that case. When that happens there will be areas on the sweep where contact is only made occasionally and eventually you will have areas at which no contact at all is made and your fuel gauge will fall to zero then. Personally I would remove the sender and check it. If the float arm wiggles easily around it is time to buy a new sender. Some say a picture is worth 1000 words. I'm sending you 5. Please look at the first one. That shows the orientation your sender rod is supposed to have. Image 2 shows what happens when it wears out...you can see the slant. Image 3 shows where the wiper is supposed to ride. Image 4 shows where it rides when things wear out. This sender came out of my 1952 pickup where it had fallen apart inside the tank. If you need a new sender I've had really good luck with those I've bought from an eBay seller (id is Renbusan): https://tinyurl.com/y3lhydzg This 0-30 ohm sender is what you'll need and I prefer this one because the rheostat is a flat plane (not curved), the rheostat contacts are molded in place, plus the 0 ohm reading is 0 and the 30 ohm reading is 30. Be very careful buying a replacement unit if you need one. One popular seller of parts (whose name I won't mention) sold me one which actually was a 0-90 ohm unit on which somebody who made it had dribbled solder to reduce the overall resistance to "about" 30 ohms. That meant at points you had no idea how much fuel you had because those areas which had the solder applied registered the same ohms until the wiper got to the point where contact was made with a good part of the coil. You can see what I found when I took it apart to figure out why it wouldn't work in the final image. Good luck!
~ Jon 1952 1/2 ton with 1959 235 | T5 with 3.07 rear end