Honda eu2000i 12v outlet for fan?

romore wrote:
That is correct. The generator produces unregulated AC which is rectified to DC, this circuit supplies the 12V outlet. It is then inverted to 120 VAC 60Hz. If power is bled off the DC circuit a low voltage signal will go to the inverter producing the wrong output.

The schematic indicates there is a totally separate winding on the transformer for the 12 volts, which then is taken out from the bridge directly to the connector. Other than the thermal load issue if you were loading the A.C. to the maximum, which would defeat the overload protection, there is no interaction between the two circuits. You can use both outputs at once.
I'd be a bit nervous about the voltage, which is significantly higher than 12 volts. When I measured mine it was more like 17 volts. If nothing else add a capacitor for a bit of filtering and accept the fan may not live too long with the high voltage.