One thing I'd try in the interim. Looks like the female connector goes up the mast, with some possibly dodgy wires on it. If that connector has some sort of setscrew that holds it to the wires, try removing it, and look at the ends of those 4 (?) wires, see if highly corroded. You may be able to resurrect that connector. Clean with contact cleaner if needed, and then use a 12V battery or other 12V DC source (power brick if you have one) to check each of the 3 power wires - not sure which wire (maybe wires?) is ground. See if you can light the bulbs. I'd open the fixtures at the masthead anyway and inspect - look at the wires going into those sockets, the state of the sockets where the bulbs go in, etc. Examine the bulbs, maybe test them directly with 12V to see if they are good. That will at least get you to the point where you know that the wiring from the plug on up to the bulbs works, You should be able to see which wire colors attach to what on the masthead, and what type of bulbs (possibly bayonet where the metal surround on the bulb is usually ground, and the dimple on the bulb bottom is hot). What mast lights do you have - maybe an anchor light and steaming light? You could try that with the running lights too. In any case, I'd inspect the light fixtures and bulbs no matter what.