All I could find was this: Patent No. 166843 (31-01-1934)
Inventor/s: FABRIQUE D HORLOGERIE LA CHAMP [CH] (FABRIQUE D'HORLOGERIE "LA CHAMPAGNE" LOUIS MUELLER & CIE. S. A)
Applicants: HORLOGERIE LA CHAMPAGNE LOUI [CH] (FABRIQUE D'HORLOGERIE "LA CHAMPAGNE" LOUIS MUELLER & CIE. S. A)
Watch case serial number of belonging t the movement is 5258933, so we should date this to at least 1934 I guess.
So I assume that the part at the back acts as a pendulum and swings side to side ever so slightly, winding the main barrel spring.
Photo supplied by member esk51
Ok, a bit more info on this movement. Designed by Louis Müller and marketed in watches by Louis Müller & Cie, Bulova used this movt briefly in the 'Champ' model. Further digging reveals that another name for this company is Fabrique d'Horlogerie La Champagne.
They were also well known for the 'Wig Wag' automatic watch movt.
Dates for the patent appear to be early 30's and Bulova examples date to 1936. (Square stamp) This movement had a movable stud carrier (rare for the time) and Breguet overcoil.
Other names used by Müller are Dido, Mars, Aster, and Champ. I have said elsewhere that this was based on the FHF 29, but the keyless works are very different, so this is incorrect.
You can clearly see the calibre number stamped above, 28-20, which is the Champagne calibre. Despite this, it is my experience now that not all parts are interchangeable with the Bulova 13AP, particularly the balance. It was very common for Bulova to mod the balances on their ebauche based movts, and they obviously started doing this very early on.
From the Watch-Wiki:
"La Champagne SA
ENTERED INTO DATABASE ON 11/02/2011 Found in new model identified as "Champ" or "Astor". Possible "Shield" datecode. Datecode not verified.