Curious. Is there any historical reason for the lack of electric traction in the South Island? (Like separate companies at one time, maybe?)
In Britain it was traditionally London and the the part of England immediately to its south which was heavily electric.
London has the Underground, of course, which despite the name actually has about two-thirds of its tracks at grade level!
The old Southern Railway, (later the Southern Region of British Railways after nationalization) used 3rd rail electrification. The S.R. lines run down to the south coast and were always very dependent upon London commuter traffic, so with relatively short spaces between stations and frequent stops electric traction was ideal.
There were overhead electrification schemes in other regions, of course, but it was only in more recent years that most of the main lines running out of London in other directions were electrified.