I did the research on this thing, but it will stump a few of you anyway.  The answer will blow you away.  One vacuum tube in it and some other electronics.  Early 60's dating, and that's all the hints you get....

DM&FS

Looks like it sends or receives a signal. To test car radios or to operate remote control device.

Nice butt hinge template.

My guess is a power supply

my swag... garage door opener control?

The one that just sold on Ebay for $12,  was called a garage door opener.
Mel

Probably uses more power than the garage door itself....

And here I thought it was a nutcracker

Yes, the transmitter portion of a first generation garage door opener.  Imagine waiting for that tube to warm up before you could get out of the garage in the morning!!.  I found someone that had the very same question I had on a vintage Cadillac forum.  His was mounted right behind the radiator of his '62 Fleetwood.  Container didn't look all that waterproof to me.  I will tell the new owner about the $12 winning bid.  Me?  I'd keep it for a conversation piece.....

DM&FS

Yep: when I had the chance, I kept an oldie that a friend took out of his grandparent's house after they passed on, close to 30 years ago. 
It doesn't look like I'll get rich off of E-Bay, then, since I've only got two transmitters (run on 6 V DC), and I think three receivers.  The transmitters have the same sort of V-shaped antenna, but aren't marked on the outside of the boxes.  I have three old door mechanisms; the oldest-looking one is a "Auto Magic" door operator from the United States Motor Corporation of Oshkosh Wisconsin.  There are newspaper ads from 1957 offering one as a prize in a contest, apparently.  The serial number on one of mine appears to end in "...54", which makes me think that it might be the year?

Cool.  I've never understood the serial number game on anything except maybe the old VW Beetles....lol

thanks

DM&FS