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.
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Whitebait Season starts 1 September 2026 and ends 30 October (inclusive). Chatham Islands: 1 December to the last day of February (inclusive)