The Pearling Tool is a hand-operated fly cutter used with a indexing wheel for guilloché style embellishments. It is a variation of the Eccentric Cutting Frame.
Some believe that it was used to make the pearl-looking balls around the periphery of the object that you see in the picture to the left, though there are no references to this in John Jacob Holtzapffel's book, Turning and Mechanical Manipulation, vol. 5 - The Principles and Practice of Ornamental or Complex Turning (1884).
In fact, there are only vague references to this tool anywhere, making it seem to be more mythical than real. Some in the ornamental turning community think this is a term that was applied to another tool, but others disagree. In any regard, as shown in the picture above, this tool has been made at one point (I think it was by Lindow Machine Works), but I cannot find any sources for them as of 2019. If you really want one, contact David Lindow.
The video from Ed Davidson (AKA, YoYoSpin), Embellishing Cabochons with the Rose Engine, shows this in action, around 11:00 in the video.
As a final note, what is more likely to have been used to make the "pearls" shown in Figure 530 is a pearling drill bit like the one to the right. You can get one (or other, similar ones) from Chris Ploof at Ornamental Tools.