That bulb is an HID , not the standard H7 bulb. Plugs into a transformer ballast that then either connects to the stock h7 connector or a dedicated wiring source.
To rule out the start switch as the problem, start bike and put in reverse. If lights come on, then it's start switch. If not, then check fuse and swap headlight relay with known working relay in relay stack.
That depends on who/where you buy them from.There is one ballast per lamp. Ballasts are a problem but a bad ballast will effect only one lamp at a time.
The person that installed the HID system may have also installed a headlight cutout relay. You will need to find that modification and test it to make sure power is being supplied.