Interesting lens. Since the catalog shows a rimset shutter and the one on eBay is in a dialset, I'd guess the one for sale is earlier---they probably shuffled the available focal lengths around a bit over the years. (The catalog seems to be from the 1920s, since it describes Ilex as having been founded "over a decade ago".)

Someone on LFF speculated that these might be derivatives of the Protar, based on the maximum aperture. I've got a Gundlach Radar XWA that's also f/16 and might be a similar design, and it's a very nice lens---focussing at f/16 is a challenge in anything short of full sun, though.

That separation does look pretty scary. I'd probably pass on it myself.