Ok, I might be wrong on that. I've never pulled one apart myself.
After more research the Eagle probably uses a grease or mineral oil in the gauge that dries out. The capacitor would be inside the gauge itself and require disassembly, and so would replacing the grease.
Those are the four basic ways to dampen gauges. Some sending units have enclosed floats with little holes to prevent fuel sloshing around the float. Others like ours have the lever style we have there is no practical way to dampen the sending unit, so it has to be in the gauge. There's the capacitor method to even out the electric signal, and some new cars just use the computer to even it out.
If you want to build your own, then I'm seeing a 2,000 mf between the sender line and a ground being recommended. A capacitor is in essence a small storage device and a big one like that will even out the signal by charging and discharging. I haven't done electric component math since college, so I'm not going to claim I verified that.
There are two kinds of gauges, one that's heated by a bi-metallic spring and another that uses two opposing magnetic coils. The spring style needs no dampening because of the rate it heats and cools. The magnetic style moves quickly on its own unless dampened, and can vibrate if the voltage regulator (CVR) on the cluster is bad.
There is definitely some kind of dampening involved, but it's apparently something they don't want you to know about. I can't even find that mentioned in my TSMs. They go from the CVR vibration, which can be slower then you think, to the "Fuel gauge wavers over rough road" as a "normal condition", which is way on the other side of the problem.
If you have what I have, that the fuel gauge continues to seek around the actual level due to sloshing after a stop, or quick movement, but not noticeably on level highway or when the car hasn't moved for a few minutes, its the dampening in the gauge. I just want to clear that up in case I might be misinterpreting your symptoms.