I expect bunny trails away from the question asked. Many different trade experienced people from all over the world have the opportunity to respond.In the scenario where the current flows over the jumper from the Utility neutral to the fence, the question would be which one is the source and which one is the load. It's easy to assume the Utility neutral is at a higher voltage relative to the fence. But in the scientific method, both assumptions are valid (or would have to be listed as possibly true). Both would be tested, but only one would be tested and proven true.
Dan said it better. One side or the other has to be the source. Using harmonic distortion ranging from 4-8%, a phase contact is suspected. The fence being the source in this N-E connection has been seen before. The complaint is from a pool owner, so 10V is not going to be the acceptable threshold.
In the early morning, with a lightly loaded POCO line, there is a N-E of 5V. In most stray voltage investigations a loaded single phase POCO line or pipeline rectifiers are usually the first suspects to rule out. I think this has been done.