I've worked with mimeograph machines well back into my high school days. Ordinarily I've typed onto the stencil, but sometimes writing is called for, or perhaps a drawing. A stylus like this one comes in handy when that's called for. The rounded head is supposed to prevent tearing of the stencil, though experience teaches that it's far from a fail-proof method.

But I doubt that I could find a mimeograph machine that uses the sort of stencils for which this stylus is designed. Today preparation of the stencil is done through photocopying the original onto a special sort of stencil, and the stylus, as much as I loved having it available to me, is no longer needed.