This is an Eberhard Faber Mongol cap and extender (with an A.W. Faber No. 3 pencil).

But it’s not quite the extender in this advertisement:

Most of the paint has been worn off but the Mongol band is still distinct, and the sliding ring works perfectly; not bad for being around 100 years old (same goes for the pencil). I think I’d like to paint this black again and restore it but I’m not sure what kind of paint to use.

My first idea would have been to use the kind of paint used for scale models, but that might be too thick a layer for your restoration. 8^(
Thanks, Memm. I’m going to take a look at some car touch-up paint, or just some matte enamel.
Car paint sounds like a good idea!