I hope I'm not butting-in on the discussion.
Normally, one wire on the field terminal and one wire on the armature.
With an add-on noise suppression capacitor, add wire to armature terminal.
The capacitor body is ground and is grounded through the clamp and body of the generator.
From the picture it looks like one terminal is grounded. Doesn't look right to me.
One way to check if the unknown device is a cut-out or capacitor, remove wires and measure resistance (ohms) with meter.
A cut-out will measure 0 resistance. If using a digital meter nearly 0 resistance.
A capacitor will measure low resistance (may need an analog voltmeter) as it begins charging (meter deflection or change) and measure high resistance when charged (if the capacitor is not dead).
