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From research (I haven't had the opportunity to verify this yet), the fuel gauge axle is suspended by a bearing. From the factory, the bearing is charged with a viscose silicone or fluorocarbon gel fluid (picture a super tacky, clear, greaselike substance) exhibiting ultra-high shear strength. Dampening (aka, damping) fluid is used to create rotational drag on gauge axles in order to retard needle deflection rate. Eventually, the fluid dissipates and loses effectiveness at which point the gauge needle dances in sync with fuel slosh in the tank. Watch the linked YouTube video comparison of a used vs new fuel gauge.
I have never seen a speedo that was connected with any kind of spring. Normally they work with a magnet spinning inside a cup. The cable drives the magnet and as the magnet spins inside the cup( which is connected to the speedo needle) it draws the cup along and based on how fast the magnet is spinning the needle indicates your speed. My experience with a bouncing needle is the cable has an issue.