It could be a 12V AC adapter. Not too common, but they do exist. Four of the myriad diodes would be connected in a bridge rectifier to convert the AC to DC. (I don't see any smoothing capacitors though....)

Depending on how creative you wanted to get, a clock might be designed to run directly on a pulsating rectified DC supply. That would give you a sort of baseband embedded clock signal at 120 Hz. Or use two half-wave rectifiers and design the whole clock based on trinary logic, +12V/0/-12V.

Realistically, since the mains connection is hidden behind the frame, it would be easy to tap off internally a connection to the 12V AC signal from the secondary of the transformer, before it gets rectified and filtered to DC.