In 2002 there was an exhibition at the Bergstrom-Mahler-Museum, showing the 2002 Perthshire designs - which never went into production, but obviously had some samples done in 2001, before the studio was closed. Apart from new designs, also a few continued designs are shown in the exhibition leaflet - including an "Aladdin's Cave", described as "Crushed millefiori set on two layers and set on a black background. 2-3/4" diameter."
Now ... this is not an official Perthshire catalogue - so no proof that this design was called "Aladdin's Cave" by the studio.
The design doesn't show up in my collection of post-1997 Perthshire catalogues (which isn't quite complete, though) ... so it's difficult to tell whether it had been produced continuously (and just not mentioned in the catalogues) - or had been discontinued and taken up again for 2002. Even that cannot be taken for granted, as "Aladdin's Cave" is just mentioned (together with Marble and Pyramid) as "Related Objects" - no specific year given.
If you are interested in Derek Carter's detective story of chasing up high quality images (I only had a poor scan of a multiply folded leaflet), read the PCC Newsletter 101 of November 2009.