Jewels,
The picture in post #11 of your overheads shows a 3-wire system.
The incoming power has three wires, 2 hots and a neutral.
That will be entering your weather head and going to your meter base through the conduit mast.
At the meter base the incoming neutral will be bonded (joined) to the grounding conductor that is connected to your ground rod.
From the meter base to the panel there will now be 4 conductors, 2 hots a neutral and a ground.
The same picture shows a free air cable that is traveling up the outside of your mast that is the feed to the lower overhead that feeds your remote sub-panel.
That shows that there are only 3 conductors in that overhead.
In a perfect world, there would be 4 conductors in that overhead, 2 hots, a neutral and a separate ground.
That is not the case here. If you care what to call that uninsulated overhead wire, you will need to follow the feed cable for the sub-panel back to the main panel and see where it is landed. Either on the neutral bus or the ground bus.
(But at that point they are electrically the same point, and it doesn't make a difference what we call it.)
The moral of the story is that it was very common at one point in history, to just use a 3 wire overhead to install a remote sub-panel. In fact, it was common to drive a separate ground rod to ground the sub-panel. This is not the currently approved method. It will create what is called ground loops, but that is a whole different topic.
All of that to say, that this has nothing to do with the fact that your light isn't working.
Is your out building's sub-panel wired up to current NEC code? No
Does that have anything to do with why your light is not working? No
So, how do we troubleshoot your light issue?
I would first recommend moving your light to a known functional outlet and see if your light works there.
This will prove if the problem is just in the light or in the outlet.
If the light works properly in a different outlet, then next I would use your meter as
@M48 suggested to take voltage readings at the outlet in question.
Report back what you find, and we will go from there.
I hope that help clarify things. We'll get it figured out!
Cheers,
WillieP