If you want to slow the swinging on an older fuel gauge, you add a capacitor, not a resistor to the signal wire.
The device is a varistor, essentially. So, if you change the resistance, it'll change what you display on the gauge. If you add a capacitor, it'll smooth the peaks and valleys (what you see as swinging) on the gauge. New gauges (pre-computer) have said capacitor in them, post-computer it's waveform generated to be smoothed.
I usually install a 1.5f, 15v on customer cars when we do a restomod. If you want even less responsive more farads, more responsive fewer farads. They're available from Amazon or anywhere else (Digikey, Mouser, etc) for a few pennies a piece (buying small quantity, unit price will obviously go up)
On my personal square? It waves to me on its way down. My wife laughs whenever we take the truck out. I haven't done it yet on most of my old cars. Some there's no point (like the Square; I have two tanks, and an average is just fine, thanks), some I just haven't restored them yet. I'll do it when the cluster is out and getting worked on.
Feel free to experiment. You won't break it, as long as the voltage is 15v or greater. You don't want that thing going bang under your dashboard.
No harm, just a really loud pop.