Harvest power from an electric fence

Those fence chargers usually generate a high voltage spike on the wire fence, relative to ground. The wire fence is on insulators to make sure that almost no current flows, unless something touches it. I've heard that wet grass leaning on them can draw enough current to effectively neutralize such a fence.

So here's the take-away: there isn't so much a current through the wire as there is a voltage on the wire (capacitive charging currents neglected). So if you connected one end of the high-voltage side of a flyback transformer to the fence, and the other end of same winding to ground, you ought to be able to pick off slugs of current on the low-voltage side of the transformer, at a reduced voltage.

Caveat if you try this with a flyback liberated from an old CRT: they often embed a diode in series with the HV winding in those units, and they're usually potted, too.

Possibly.

I live on a small horse farm and recently made a fence tester using a resistor and a small neon bulb. Even with 10k resistor, I get a really bright flash from the bulb: clearly visible in broad daylight.

The thing I'd want to be careful with is how you get power off the line: intuition says wrap a few turns of insulate wire around it, but that will make a step up transformer and give even more voltage.

If I get a chance tonight I'll try to see if I can power an LED with a single turn around the fence's hot wire.

I'd try connecting a small transformer (one designed for a flyback power-supply) with a high step-down ratio between the energized cable and ground, you could then rectify the output and do whatever with it. The HV coil impedance should be high enough to avoid a tremendous draw on the cattle killer, but I don't know much about them. It may take a long while to charge a battery, but possible. If you just want to power a sensor, I'd use a capacitor.