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There are tests that can be performed that create no liability.
Already performed is turning off the customer's main breaker. No major source of current from the customer's home.
With the customer's main breaker off how large is the current on the customer's GEC, and simultaneously on the customer's neutral from the power company transformer? Are these two currents in phase or out of phase? In other words is the current coming in on the customer's neutral the same current as is going out on the GEC?
What is the voltage drop from the power company's ground rod at the power company's transformer to the customer's neutral bus in the customer's main panel? With an ungrounded delta supply as I am serviced by at my home the transformer ground rod is unique as a transformer grounding point for me and my next door neighbor, the only ones on the transformer. For a wye primary source there are many transformers with their own ground rods and all secondary neutrals connected together by wire and the ground rods and common to all home neutrals. Both primary and secondary neutrals are tied together. A much more complex neutral system, and there may be a water pipe connection between neutrals of homes.
As an approximation under normal home load conditions I would expect a voltage difference between the transformer ground rod and the home's main panel neutral bus of greater than 1 V to be excessive. If at the transformer the transformer neutral terminal is good to the transformer center tap, and from the terminal to ground rod is also good, then the voltage drop ftom transformer center tap to ground rod can considered to be in the millivolt range for likely neutral currents. Thus, using the ground rod as a voltage reference point is like being at the actual transformer center tap. Ground rod resistance to earth is likely not less than 1 ohm, and usually much higher.
If the neutral conductive path, intended wires, is of a high resistance, then at least some neutral current flows out thru the earth and water pipe paths.
Voltage drop and current measurements should allow you to identify the problem without opening anything except previously said main breaker.
You can also make voltage measurements from the transformer ground rod to the home's siding to try to determine the source.
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