the relay has 2 male 900x connectors and only 1 female 900x connector.
You only plug in 1 factory 900x headlamp connector, drivers/pass does not matter. That's all that's required to "trigger" the relay. Once triggered, it draws power from the direct ground and (+) battery, firing up both ballasts via the 2 male 900x connectors you've attached to the ballast itself, or short extension wire.
Both are not required, as only a small amount of voltage is required to trigger the relay.
The free/unattached male 900x factory connector, I suggest you glob some electrolytic grease on it and tape it up out of the way so it does not get corroded.