Yeah that soft black bit is the fusible link.
Sometimes they blow and there is no external indication such as burnt insulation.
Used to give the fusible link a pull test to ensure that it was intact.
Often the pull test would show that it had blown.
I think it may have been an ADR requirement for the headlights to have circuit breaker if the beams werent individually fused.
The idea being that if there was a short, the breaker would trip then reset hopefully giving enough light to get you safely stopped.
Had that issue once in a Commodore years ago.
I had fitted driving lights using the large New Era tin can relays.
The relay shorted tripping the headlight breaker. It reset fairly quickly. Did it a couple of times before I found somewhere to pull over.
Never used those relays again after that.
Cheers
Rob