Speedo going mad and whining

I would try a good greasing job first before you start changing parts.

Maybe I should explain a bit more. I had to do with a Renault R4 where the speedo acted normal until i reached 60 km/h or so when it suddenly started to scream and the needle went haywire and danced between zero and 120 even when slowing down until you came to a complete stop.
I opened the speedo which was dry inside like a desert. I found some crumbles in the corner which were grease 40 years before. I cleaned everything thoroughly and greased the moving parts. I can't remember which kind of grease I used, but I did some research not to use something which harms the plastic gearing. The speedo worked fine afterwards and still does today.