Insulation resistance tester: orders of magnitude difference in measurement depending on connection polarity
It could be geometry (pointy things spray electrons when made negative), or the copper wire could have enough of a coating of copper oxide (a semiconductor) to be rectifying the leakage current through its
insulation.

A typical gas-filled rectifying tube used a filament, but some
were simply points opposite plates (similar to the field-emission
cathodes that are still being experimented with), and still rectified.
This would be consistent with the given results if the steel of the
transformer had a rough surface compared to the copper wire,
and was field-emitting at the high points.

Copper/copper oxide is a Schottky diode structure, and copper
oxide was used for rectifiers in years past.   The leakage of practical
CuO rectifiers is 
relatively high in the reverse direction, so it took stacks of junctions in series,
but the asymmetry in conduction was maybe 100:1 between forward
and reverse bias.

A good strong screw or solder connection bypasses any
oxide, but the varnished wire in a transformer hasn't any
oxide-destroying properties.