I troubleshot a friend's boat when his stern light would not go out, even though the switch and red/green bow lights were off. Maybe it was the tequila, but after a moment's thought I asked if his son had turned on the light in the v-berth, he said "yes but it doesn't work".
His ground was broken somewhere forward of the mast
, isolating the what was supposed to be the ground for the front cabin
and forward nav lights. The resulting circuit, with the cabin
light switched "on", was:
+12V supply to v-berth light "+", v-berth light "-" to fwd nav lights "-", through both nav lights in parallel, nav light "+" to stern nav light "+" finally to stern nav light ground.
With the two forward nav lights in parallel, neither conducted enough current
to light noticeably, and the higher wattage / lower resistance of the v-berth cabin light let the stern light get most of the voltage. Added a ground jumper to the fwd cabin light, and voila, no more mystery stern light.
In this case, I'd look for a bad ground, likely at the mast
between the lights. I've seen boats wired with two masthead bulbs so the forward one alone serves as a steaming light and both together make an anchor
light (at the cost of double the current
drain while anchored). The LED bulb might get enough current to light via pilot lights in the electrical
panel, if any.