The peak is just over 12V - it could easily average 12V with either a series resistor to drop a bit, or a slightly undersized capacitor. I just chose a 2200uF cap for it, so I'll go with the series resistor.
I just noticed that the service manual has a memo attached addressing this - the original fan was discontinued and they describe replacing it with a DC fan: direct replacement, disabling the three-phase oscillator, for some serial numbers, and adding a 22 ohm resistor in series for others. Nothing about a capacitor; they must have selected a replacement fan which doesn't need it.