It kind of scares us, frankly.

they do have a picture with the back open. it's full of capacitors.

I'm probably getting hung up on the shape and symbol in the center, but it reminds me of a Rubidium clock.

ok I have no idea what this thing is but I got really curious, here's some shit:

• this page claims to have catalogs for 1951 and 1960 Aerovox products. You'll notice that the 1951 version has the same brand logo seen in the capacitor in the ebay listing, but the 1960 does not -- that makes me fairly sure that this computer was pre-1960.
• According to this site, Aerovox was founded in 1924, which I guess gives you a farthest back era, though that's hardly surprising given the history of computers. More importantly it could mark this as a bit of wireless equipment, but who knows if they just manufactured the capacitors.
• given the LACK of material inside, my personal theory is this is a sort of readout for a more complicated device -- likely this was part of a kit, with other devices that would do the Thinking, and this would be the readout. Some sort of radio machine?
• friend of mine (@coolranchzaku) who is an electrician says the circular thing on the back side is almost certainly a potentiometer, which would adjust the voltage from the wall jack into what works for the device.
• @vogon has put forward that it might be a movie prop from the 50s or 60s, hence the old capacitators but unclear usage. 8 sets of resistors & capacitors for 8 lights, on random blinks. I am not swayed by this theory, but he's very convinced.
• I think it's some sort of endpoint for a computer device. The rear power cable could be also some sort of bundle (as per @coolranchzaku) that provides some sort of basic data. But he's pretty unsure about this.

simplest explanation is that it is a blinkenlights machine for a movie prop. could be some sort of terminal for a larger computer machine. i dunno!

i'm completely fascinated by how TILT is a recognizable thing but none of the others are. if anything that makes it seem less likely to be a movie prop? it's such an arbitrary decision but definitely something that could happen for a device with real purpose

(they could've just copied something else though)

The seller didn't think it was worthwhile to take a single picture of the plug, yet was able to trivially plug it in. That tells me that it is just an ordinary power plug. The only input is power, the only output is random blinks. The movie prop theory sounds good to me. The only thing that it's missing is a secret control to switch between "happy blinks" and "the tilt light is mad" patterns.

i think this is a dog. its whats dogs look like

Movie prop makes sense, and I even figured out how it works.

AC comes in, goes through a diode, filtered by the big yellow cap. Now you have about 170VDC.

DC goes through the potentiometer, which limits current to the rest of the circuit.

The rest of the circuit is just the same thing in parallel, eight times:

A resistor in series with a capacitor, so it charges slowly. A neon lamp across the capacitor.

A neon lamp is a gas discharge tube, with a breakdown voltage. When the capacitor voltage exceeds the breakdown voltage, the lamp flashes and discharges the capacitor, starting the cycle over.

Since the parts have loose tolerances, the frequency of each flashing light is going to be slightly out of sync and the thing looks random.

Turning the pot adjusts the blinkyness speed.

So yeah, movie prop, or stage prop, or just a funny decoration for your house if you're That Kind Of Person.