If assuming you have your lights, one A and one B in parallel, you disconnect A and turn on B, or switch on B and turn on A, it is because the power is poor; that is, not enough current arrives. You can use two lower voltage Xenon or use another source. But if it is as you say that it only happens with one, try to try the one that does not turn on the one that does, to rule out that it is short. I suspect you have a short circuit in which you disconnect to turn on the other.