I'd have to see a picture in order to advise.  I used to own a vintage toaster with an in-line cord switch.  It wasn't an automatic, though.

Wow!  That's an early version of an automatic toaster for sure.  I'm going to guess that the "automatic" cycle was controlled by a clockwork timer and that this unfortunately is no longer working on yours.  

Very cool toaster - what a thoughtful gift!!

I agree with Paul.  I had a vintage "Toastwell" and the ticking of the timer was audible on that one.  Since it's likely a mechanical timer, it might just need a cleaning to get it working again.

Well, there's nothing automatic about a toaster that needs human intervention to keep it from starting a fire.  Seeing as how the manufacturer made the claim of it being "entirely automatic," it seems to me that you should be able to set it and forget it.

If the timer is working, it's possible that a key piece of the mechanism that would trigger a break in the heating circuit isn't functioning or has broken.  If you can get the exterior off so you can examine the timer and identify the shut-off mechanism, you shouldn't have to disassemble it any further to make the needed repair.

If the shut-off proved to be a weak link with these toasters, that could be why you're finding pictures with in-line cord switches.  That was cheaper than buying a new toaster back in those days.

I can see how the automatic opening would distance the toasted bread from the heating elements and keep it warm, but agree that in such a scenario the bottom area of the bread would remain in close enough proximity to the heat source to keep toasting.

I'm surprised Thomas A(hole) Edison would extend his endorsement of such a flawed system, though.