At first glance, this bead does not look like a 'typical Idar-Oberstein agate bead'.
That is because the typical beads that we see as Idar-Oberstein beads are those that were made from (mostly) Brazilian agate that was used to make beads in Idar-Oberstein since the 1830's.

Before they started using these types of stones, the Idar-Oberstein region already had a history of cutting agates and other locally found stones. These stones were generally of a different type than the Brazilian ones with quite a different appearance. The first record of agate cutting in Idar-Oberstein goes back as far as 1454.

So it is possible that this is an 'older generation' stone bead, cut and sourced from Idar-Oberstein. This would fit with the timeline that is suggested. I have not seen examples of any older beads (before the Brazilian agate) in the Idar-Oberstein museums, so that makes it difficult to really know anything about beads from that time period for sure.

I am no stone expert, but I would agree with Frank that it looks more like jasper than agate.