marda81, glad you found the problem. The ice pick is a great tool, one of my favorites. That and it’s just plain cool.
Finding a short or break in the wire is like a broken water pipe.
You start at one end or the other and work you way up the line, until there is no juice.
I have used the ice pick to puncture the plastic in the wire and run it into the wire to see if the light comes on, then sealed it back with silicone.
Don’t think I would use it for a bare wire.
Silicone does not stick to everything, this including silicone.
So using it on bare wire would be, .......... risky.

I have used epoxy inside light fixtures to protect the bare wires, LEDs but they were protected from anything hitting them.
They make a paint on plastic, that is supposed to seal bare wire, but I have never used it.
The shrink wrap like Botzman suggested works great, even on bare wire, but you need an end to slip it over, or cut it.
You might be able to get one end out of the light fixture and work it from there.
This would be
"MY" fix.
I doubt you can buy the wire from HD, they sell the ends and the connectors, but not that whole wire.
I have ask while doing my fender.
It is pretty easy to make a new one, although putting on the ends is a little tricky.
This is of course the best way to fix it.
Good luck, let us know.