Sound like a lamp failure, just replace the headlight Lamp, although it might pay to replace the pair, as they might be a slightly different colour if you do just the one
I'd put the non-working one in the working side first to see if it is the lamp before you buy any replacements, then you'll know if it's the lamp or the ignitor.
New lamps (bulbs) aren't expensive, I would go down that route first, change them over and if by chance that is not the problem, worst you have is spare lamps,
swap ignitors over , to rule them out
then swap bulb. Hopefully this works
if the top 2 hasnt worked probs the ballast filled with water, bumper off head, light unit out as its on under side
New lamps (bulbs) aren't expensive, I would go down that route first, change them over and if by chance that is not the problem, worst you have is spare lamps,
Without doubt the bulbs gone and the longer you leave it the more risk you run of damaging the ignition.
I recently had the same issue and was quoted £248.66 by the main dealer to supply and fit a replacement bulb - they wanted the bulb £191 to supply the bulb only.
The recommendation is to fit the Xenons in pairs so I bought the Osram Nightbreaker DS2 two bulb pack from Amazon for £76.
Fitting is a pain in the area and best done with wheel off but plenty of videos on YouTube if you look - hope you get it sorted
Thanks,
It work again this evening for a few minutes, was bluer in colour before going put again.
I have order from Amazon a pair of new bulbs, the Osram DS2 Laser, 200% brighter, as they weren't good anyway. Failing that the igniter after.
Remember doing normal bulbs on my old Z4, a faff with the wheel on.