Having trouble getting Amoeba pet

[Pluton, King of the Underworld]

So I tried pacifying the amoebas and waited 50 years and wasn't able to get it, but I read posts from people saying they got it in their first 10 years.

Is there a thing you have to do to get the event to show up? Or is it entirely random?

[mcsproot]

It's a separate anomaly.

[Red Dox]

You find a baby amoeba in an anomaly which then imprints on your science vessel. You will get a choice what to do with this baby duckling. If you want it as a pet, you better not dissect it ;)

[NixBoxDone]

I'd say not dissecting anything you want to stick around as a pet would be elementary. :D