I would assume, not sure how to tell, the pilot current is small now. It use to pull about 3 amps when the stock 35 watt halogens were there. Now, those connectors just provide 12v to the relay then the relay provides the power to the ballast. Not sure how much current a relay draws.
So, I now realized I described my setup wrong at first. oops. I would want the capacitor to be between the signal output for the headlights and the relay. Pretty much keeping the relay running the ballast during the brief loss of power.
I know my ballast are DC in and the output is somewhere around 30-50k volts. not sure if its AC/DC. There is a firing sequence that is built into the ballast for starting the HID bulbs and if not shielded, it messes with radios, tire pressure monitoring, and other frequencies.
Im willing to try a 1000 uf cap and diode setup depending on the relay current.