Re: I am sure there are many similar stories
"you could hear the click-click-click of them working just by picking up handset - Modem baulked at this however finding the offending fence/farmer was far more tricky than the diagnosis."
This was a double-barrelled problem - the electric fence in question would run alongside the phone line AND have live grass growing against it (which is what gave the discharge noise), but the _actual_ fault was in the phone line - something causing it to be unbalanced and sensitive to longitudinal noise (usually a bad joint or partial earth).
Many electric fence noise problems were temporarily cured with a sprayer full of roundup along the fenceline.