Dynamic spotlight always facing one way and not its GameObject's

Hello,

I'm having one of the weirdest issues I've ever had with Unity (and that's saying something!). I'm making a night driving prototype where you drive a car with a single spotlight as headlights. The spotlight is one of the car chassis's children and is the simplest it can be:

In game, this spotlight is weirdly always facing right! (-x axis). If I pause the game, the spotlight is aligned with the car's direction, as it should be, but its light shines on the right. It follows the car alright, it's not stuck on the start point. But it's always facing -x.

It looks like this - it's a view from the car interior as it's facing -z while the spotlight shines on the right: (sorry about the poor paint edit) Driving and turning the car moves the light but does not rotate it.

Does anyone have an idea why would this happen? I've tried rebaking lightmaps, adjusting various parameters on the spot, and trying other lights, and it looks like not a single one (directional excepted) can really cast light on the +x direction.

Thanks in advance