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human
[ATLA] Did Zuko just get lucky?

At the start of the series Zuko was hunting for the Avatar, and just so happened to be close enough to see the burst of bright light shoot into the sky when Katara broke the iceberg Aang was in, which allowed him to quickly find Aang when the flare went up from he booby trapped ship. My question is, was there a reason or a clue point him towards looking for the Avatar in the South Pole (e.g. a report or a rumour of an airbender escaping in that direction after the airbender genocide) was he searching everywhere and just got lucky by being in the right spot at the right time?
gpt
The Fire Nation knew the following:

- The Avatar was living at the southern air temple.
- The Avatar was not killed during the genocide, since no new Avatar was born to the Water tribe.
- The Avatar was not hiding out somewhere else in the world, since if he was he would have drawn attention to himself.

That left indefinite hiding in the south pole as the most likely option.  Zuko probably expected an elderly hermit with a broken spirit who had given up on the world.