It does look like one of DB's ring vases. They were made by using the standard Caithness cylinder vase moulds and adding the rings by hand afterwards.
Short lived design from early 1960's due to production problems ie. smoothing the rings resulting in many seconds. Mine wasn't signed either
Hard to come by but mostly found in Peat (brown) - occasionally moss (green), or loch (blue) and sometimes with contrasting or clear rings. Also available as lamp base
All courtesy of M Hills book
hope it helps