speedometer needle

You didn't say what speedometer. In most cases... the tringle like flag opposite the needle center is a counter balance. More of a place for counter balance. Once the needle is removed you will see a dab of white epoxy on the underside of that flag.
Bend the flag, epoxy breaks off, counter balance lost. This happens too easily.
I use a long thin surgical clamp ( forget the name of it ) to grasp the tube beneath the screen and work it off the stem.