Wiggling needles in O.S. engines have not been a typical difficulty. Usually, we've found it's because an extension on the needle is being moved around by the engine's vibration. This is especially so if some kind of knob is on the end of the extension.

A common 'cure' is to put a piece of fuel tubing over the needle and then reinstall the needle. This puts some tension on the needle and the wiggling goes away. On some older engines, the piece of tubing was installed by the factory.

A wiggling needle can deform the needle seat in the carburetor, so changing to a needle with a slightly-different taper can 'solve' the problem for a time. If it persists long enough, the needle seat can become deformed enough that the carburetor body will have to be replaced. A polished ring round the pointy part of the needle indicates that it's either been over-tightened when it's been closed, or it's been wiggling around and striking against the needle seat.