Take the bulb out, when its cold hold it up so you see the filament and flick the bulb it could be a broken filament that separates when hot.
Check the bulb holder connections to see if they sound, you may have a loose connection that is breaking when the lamp hots up.
If that doesn't throw up anything, with the lights on check with a volt meter with black probe on ground and the red probe on the live to the light this should be battery voltage, which you should have already checked.
If this good with the black probe still in place put the red probe on the ground side of the light you should read nearly zero volts if there are any voltage above roughly .5 of a volt you have a bad earth