A very likely cause is a low battery, which could be caused by a bad stator.
When the key is turned ON, a circuit in the junction box prevents power to flow to the headlight. That allows maximum power for the starter motor. Pushing the start button engages the circuit, when the starter motor button is released, the headlight is on.
If the engine then dies, the headlight is still on. Pressing the starter button engages another circuit, killing the headlight when the button is pressed, once again for maximum power to the starter.
If the battery is low, or the junction box faulty, the circuit might not engage, leaving the engine on but headlight off. Fully charging the battery should fix the problem; also inspect the stator to see if it's bad. (Instructions in the Verses, or the sevice manual.)
Good luck! Start with charging the battery, see how it goes from there.