I *believe* the damping is performed by a capacitor and perhaps a
resistor inside the instrument. These buffer the signal so the needle
sees a slowly changing signal instead of one that fluctuates wildly as
the sender's float bobs up and down on the fuel.

Realistically, the only way to eliminate the needle movement would be to
either replace the instrument in the hopes that the next one has
slightly more buffering, or to replace the individual components on the
instrument for others with better characteristics.

I'm not sure either of the above are really practical, unless you
acquire another gauge from a wreck and install it yourself to see if
that helps. I don't think you'd like the price if you had somebody do it
for you.