How to remove cigarette lighter bulb

Can anyone explain how to remove the ciggy lighter bulb? I've got this far but can't see any clips or any way to remove the black bulb holder.

IIRC you just slide that black part off the ciggie lighter.

After a few years of my Children using it to power Ipods, and I phones it wore out so I just replaced it with  one that was off the shelf at my parts store.

Thought I was going to break something but yeah, it came off eventually. Now wondering if it's worth replacing the bulb or the whole unit like you did.