Mimic octopus?? Well, as far as I know, the word mimic implies a "monkey see; monkey do" style of immitation. Whether the term is accurate or not, I don't know. I would guess that it's a learnt behaviour.
Are you sure? I thought that imitation was an observational behaviour, damned if I can remember all the terms (and I should!!) but I was under the impression that imitation wasn't hard-wired. But then I guess the Natural World keeps throwing up things just when we think we understand something! Keeps us occupied I s'pose!
If "hardwired" behaviour turns out to be succesful in the survival game, it's nothing else but fitness and therefore perseveres in the genepool. Same goes for eyespots on bimacs, the "twig in a breeze" movement of chameleons or the ability of mimics and (likely) wonderpusses to observe and imitate. The imitation itself is based on the input of the moment and interpretation of events ("I see territorial damselfish, I must assume banded sea snake effect"), but again, the ability to perform the interpretation and act accordingly is the bit that's hardwired.
With (a two year lifespan and) no real parental care or social structure, there is not likely a meme based learning-process, as is with social animals such as our own species.
If the ability to mimic wasnt preprogrammed that would mean that there wasnt anything really separating a mimic from any other octo, there would probably be heaps of copy cat octos.
So the question is whether its repertoire is totally instinct, or if it learns the different imitations from experience. ie a mimic that had never seen a lionfish would never use the lionfish "ability". I would say its very likely the latter.
It would be a great thing to try figure out. I would imagine that the trigger for memorizing how to mimic objects would be black/white stripes.
Perhaps you might be able to get a mimic to copy something totally random, like a chess board or something. Just like ducklings following anything that waddles past when they are born in that famous experiment (cant remember by who)
What's really the interesting bit, is that the mimic octopus mimics its predators' predators. Your observation with regards to there not being multitudes of copycat octo species is very astute! It is for all intents and purposes the strongest argument for a unique built in quality.
The repertoire is built on what works in practice, so as the Lembeh straight is home to lionfish, banded sea snakes, poisonous flounders, brittle stars and mantis shrimp, that's what gets selected for. The flounder and starfish patterns are the only cases where the mimic's behaviour is pure mimicry. It uses it when it is out in the open as to avoid being eaten.