Looking at the pics I would say it's related to the ashtray. I can see the colouring is similar to the "cabbage" but it doesn't "feel" right to me. Is the bottom of the ashtray very similar to the bottom of the vase? I've had a few Italian pieces in the past and I think that might be right for this.........although none of those had a ground out pontil mark - they were all flat bottomed.
Thank you for your help - have a great weekend.