What would have been much simpler and a lot less expensive would be to put a resistor across each neon lamp. Perhaps 10K ohms, although in PLC work we use 5600 ohm resistors. It totally prevents undesired triggering .
This is a great story, with even greater educational value.
WKetel, I agree the robustness of using a high voltage system was lost by allowing it to also be a very high impedance system, as well. Ah, nothing like adding a ballast resistor from time-to-time.
If shielded wires solved the problem, then it was not a magnetic field coupling issue but an electric field issue. At power frequencies, "shielded" cables do absolutely nothing to combat magnetic field coupling. The extremely low operating current of the NE-2 means that a long wire could easily couple (capacitively) enough energy from nearby high-voltage wiring to make it glow.