They have been enigmatic from the get-go.
When discovered, scientists actually found only Female of the fish and wondered what is happening. That is when they discovered this symbiotic relationship between male and female.
However, there is more. On top of their head, like the middle of their forehead, they have a bulb-like structure. That glows in dark depths of the ocean. It works both for finding mates and same time act as a bait for fishes whom they snap up. Thus acting as a fishing rod sort of protrusion giving them their name. And that structure only glows because the source of luminescence is symbiotic bacteria that dwell in and around the esca, enclosed in a cup-shaped reflector containing crystals.