Wormley for Dunbar expert needed  

For comparison...
This is a Sheaf of What side table.

MIddle?
What is the center made of? Is there a brass ring or a wood disk? I can't tell from your photos.
I've had a lot of Dunbar including a few "Sheaf of Wheat" tables. I've seen vintage tables "in the style of" but the construction always gives away the fact that it's not really Dunbar. There is never a brass ring in the middle, usually a wood disk. That, and the absence of labels. Most Dunbar is marked (upholstered pieces were usually signed with fabric tags or in the decking, if they are reupholstered, that is often absent).
I doubt that it's really a Dunbar piece. Most likely another design "inspired" by Wormley. Dunbar did make all their furniture to order and would customize the designs for customers (sizes, finishes, etc) but I've never seen a stool like that before.

Pegboard
The band is wood, though it's not a disk. The construction seems poor. I've also never seen a Sheaf of What piece with the band in the center. Usually it seems the band is placed so that the 'sheaf' is asymmetrical.

Hate to rain on your parade
... but I really don't think it's Dunbar.
Interesting stool and still useful. Is the bottom curved or flat?
What other Dunbar pieces were there in the home?

That's okay...
I was skeptical anyhow. I purchased the piece online and will simply return it. Thank you for your help with this. It confirmed what I suspected.

Many many many of these tables with the brass band are on 1st Dibs are being advertised as Dunbar and Wormley.Are the tables with the brass band the Lane table? I have seen a seath of wheat table by Lane that is a knock off of the Dunbar.