ETOPS AKL-EZE
 

Am I right in thinking that with ETOPS 330, no diversion airports are needed for the AKL-EZE route as it is over the Pacific for less than 11 hours?

Are there in fact any practical diversion airports south of 30 degrees latitude in the South Pacific?

Not necessarily right; I don't know the numbers, but if the route does take 11 hours with two engines, it would take longer than half that time to fly half the distance on one engine, so 5.5 hours (330 minutes) doesn't get you home and dry after a mid-point failure. (All this reminds wrinklies such as me of the good 'ole days of PNR calculations.)

And I don't know the answer about usable diversions, but I suspect not, unless there's one that would help on the mainland of S America such as the airfield a few kilometres North of Punta Arenas.

Sitting there for 330 long minutes, listening to the one engine that's between you and a terrifying descent into a cold and watery grave labouring away as you trundle along, hoping like hell that it won't also stop, is my idea of extreme but avoidable mental torture. So count me out. And I hear that 420 minutes is the next victory for the bean-counters.

Great circle map Great Circle Mapper although winds likely will call for different routing. A number of airports in Chile and Argentina ...