I would use the same methods as any other surf beach. Species would be similar to the rest of the South Island just less warmer water fish around. Forget about Kingfish or Snapper that far South.
From memory the beaches around Invercargill are quite shallow and sandy, So I might even search out guts/holes at low tide and fish them over high.
Yeah i was thinking of fishing more down the tuatapere way [ right in the botom of NZ, you can almost see stuart island on a good day]
Plus tuatapere has the waiau running through it so I’d give spinning for browns a go [tonnes of 4lb+ fish last time i went there brilliant fishing spot]
I also know of a place where people used to spear blue cod and greenbone, on a rock in a massive rock pool open to the sea [secret spot ]