Well, before posting the mystery here, I had gone hunting through Henk's pdfs and found the picture below. Henk called it 'dark blue' but his stone looked greyish black. The speckles were pretty similar.
Hopefully, someone who really knows the scotch hones will chime in. Or maybe the buyer is a member and will give us a clue and a couple of nice pictures.
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The stone as shown on eBay does not strike me as a Water of Ayr stone. The Ayrshire stones have a light-to medium-blue, comet-like streaking that is very slightly buried in the darker blue matrix. The one as shown on eBay and even Henk Bros's example as shown directly above are both whiter and rounder as to the streaking and more directly on the surface.