Being presented with a battery illuminated clock, my first impression was that it probably 1930's or 40's, but after a limited search it became obvious that earlier was more probable.
|Ever Ready Advertisement 1910's|
The clock in my shop differs in several respects. The bulb is inside the case and behind the dial, and the large plano convex lens over the face leads me to believe that it was possibly a projection clock but is missing the reflecting attachment.
|Plano Convex Lens|
|Image courtesy of Bob Croswell|
These would have accepted the "remote control" pictured here and would have allowed the user to turn on the clock from bed without leaning over to flip the switch on the clock base.
You can see more details and information at:
Electrically Illuminated Clock
Night Projection "Brothel" Clock