I have that same box with a different label placement. My Dad bought it in the mid-50's when he worked as a mechanic at a Chrysler dealer, but I don't know if he bought it new or used and he's been gone for over 20 years, so I can't date it.
My Dad called it his "ignition box", as he carried all his 1/4" drive stuff in it, ignition wrenches, ignition point tools, as well as some points and condensers when he'd make a road trip to do a tuneup. Many a night or weekend I'd carry that box as a child, while he toted his timing light, tach/dwell meter and other tools in a larger open tote. After he passed away, I loaded it with all my 1/4" drive stuff, tucked it into the bottom compartment of my roller cabinet and use it to this day. I don't visit his gravesite often, but that box and his two-drawer middle section incorporated into my tool cabinet are all I need to rekindle memories.
Bill