Not sure if these pictures will help.
This pipe type pontil does not leave the same pontil scar as the ones we are used to.
Everything you said about the decorating technique sounds right.
I have seen something very similar online which does have a stopper in the top ,so i may have been misleading by saying it had not been ground for a stopper.
The one online is described as bottle,
I will try and link it to this post.
Thanks again,
Tim