Yours appears to be a larger variant—is it 13L, like the later 870/871? The case has a man’s styling IMO and is pocket watch, so just guessing size.
Here is another size variant of this layout—a tiny wristlet that wouldn’t be a practical pocket watch. Sharing, in case it is known. But yours is the true match to #21.
The Aegler caliber number pairs I haven’t matched yet.. one of these? I note 808-9 are 7J but they are 10.5L and might match 806-7.
800-1 808-9 - 10.5L 810-1 (812-3 seen with Premo branding) 814-15 816 - 10.5L
Here is # 21 in rare Hunter 7J under Rebberg Watch Co branding for US market. This US launch happened in 1914. Same timeframe as Premo in market. https://www.ebay.com/itm/124933522263
28.83mm case diameter here, so your 11L seems right. I suppose it could be up to 11.75L movement.
Thanks for the link, looks like it, interesting find for sure. The one other instance I've seen this branded Premo calibre in use was in a Premo marked Modish style sterling wristlet.
While i didn't take the movement out of the case, used non digital calipers to measure, my updated *estimate* is that the movement is either 11.5 or 11.75 ligne. The dial is ceramic.
Could this be the Rebberg 12 ligne offering? It existed, but none have been categorized visibly online. Just saying--there are other Rebberg calibers from this time in the 11 to 11.5 L space.
And I will speculate 12L must be the rarest of the Rebberg sizes. I see a mention in a 1998 NAWCC pub, but I am no longer a paying member to see if there is even a pic of the movement in the article. I've found this movement under at least 4 other brands now, but alas only as "sold."
You have, once again, found a juicy & tempting puzzle!