94 Mustang GT HID Conversion Kit Anti-Lock Brake Light

How did you wire the ballasts? Did you tap into factory wiring near the headlight area? Reason I ask is because the ABS collision sensors are in the same location as the headlamps. It's possible you tapped into a wire for the ABS system and the fluctuation in power when you turn the HID's on causes the system to fault out.

I'd review how you have it wired up and what wires you are tapping into. Ideally you should be running direct power off the battery or coil to the ballasts and using a relay tapped into the headlight low beams to turn the relays on. There are 9007 male plugs on ebay cheap to allow you to wire this up real clean so you can remove the kit when you realize you are blinding everyone else on the road with glare

Disconnect one at a time, and turn your headlights on and see if the problem disappears.

See if it only happens with one side connected, or with both disconnected