Thank you for posting the extra photos. This does conform with the one in Geoff's book.
I was lucky enough to find another version of the wall vase/pocket in Sherwood Green over the new year break, which is shaped differently and has the hole drilled lower down in the body at the back where it hangs on the wall. The base has a polished pontil that shows the way the wheel was used to grind the roughness away, but is bright to look at.
You say yours has a rough pontil. Do you mean it has been badly ground, or that it has not been ground at all?