Thanks for posting those pictures, Webster. There's sparse information to be found about Wall cameras.
According to "Motion Picture Photography: A History, 1891-1960" by Raimondo-Souto, the Wall 35mm sound-on-film camera was first launched around 1934, and was manufactured for several decades, with various improvements over the years. The entry on Wall is included in this Google books preview, and has some interesting information:
It's possible the author got the date wrong and there were earlier versions.
As Frank mentioned, they were primarily newsreel cameras, and don't seem to have been used as studio cameras.
The J.M. Wall Machine Co did produce cameras in the mid 20s for the Movietone inventors, Case and Sponable, but there's little information about those cameras, some of which may have been modified Mitchells.
The movement does look similar to the Arriflex 35BL movement, although the closer comparison seems to me to be the Moviecam (and thus Arricam) movement, which is also easily removed from the camera (unlike the BL), and shares the sloping gate design and even the wedge shaped lever.