My own research has yielded this..
Eldor Watch Co
The Eldor Watch Company was also known as Bill & Cie. The earliest listing is in 1923 when it was listed as Bill & Cie. in Bienne.
The 1924 listing was Bill & Cie, Eldor Watch Co. in Bienne with and another listing and advertisement for Eldor Watch Co. without Bill & Cie. although this advert was only for America.
A 1925 advert lists the types of watches they could supply but only for America. The Company was listed again for Bill & Cie, Eldor Watch
By 1951 the listings were for Eldor Watch Co. SA of Geneve and no mention of Bill & Cie. These listings continued from 1966 until 1973.
Brand or Model Names Used:-
All this combined with the style, it's current location (US), it's apparent age of font, 1920- early 30s ties in nicely with my research. I will have to wait to confirm this but I think I nailed it.