Almost every sky tradition in the world builds its figures by joining bright points. Two do not. In Aboriginal Australia and in the Andes, the important shapes are read from the dark: the dust lanes of the Milky Way, which block the light behind them and stand out as black forms against a bright band.
The emu is the best known of the Australian ones. Its head is the Coalsack, the dark nebula beside the Southern Cross, and its neck, body and legs run down through Scorpius and past it. In a genuinely dark sky the shape is unmistakable once it has been pointed out, and it is difficult to unsee afterwards.
This requires a sky most people alive have never had. Reading dark constellations needs the Milky Way bright enough that the gaps in it read as shapes, which means no artificial light at all. Both cultures that developed the technique lived under those conditions permanently.
The two are unrelated. There is no contact and no common ancestor within any plausible timeframe, and the shared method is a case of two peoples looking hard at the same sky under the same conditions and arriving at the same insight. Where Greek astronomy had light to work with in the Mediterranean and never needed the dark, both of these traditions used what was actually the most conspicuous feature available.