How do non contact voltage detectors work on open circuits
Because it isn't an open circuit. To AC, a capacitor is just another impedance:







simulate this circuit &ndash; Schematic created using CircuitLab

This series of capacitors and high-impedance ground completes a circuit that allows a very, very tiny current to flow, which the electronics in the NCVD will detect and show a signal.

Note that this is only one scheme; there are others that involve directly sensing electric fields that can also detect DC voltages.

This schematic should also make it clear why the neutral wire isn't detected. Neutral is ground-referenced somewhere in the system, so that would be connecting ground to ground through a bunch of passive elements.