I like your idea, but I think it's downside is that it would just operate like whatever job you're mimicking at the time.

I would suggest that mimic's copy the skills from their party members, but have unique combo effects. Say there's a Paladin, Dragoon, and White Mage in the Mimic's party. He opens by copying the Paladin's Fast blade, which he follows up with Feint from the Dragoon. Because he is a mimic those two moves combo together to result in a 5% haste buff for himself instead of any combo effect available for either of the original jobs.

The thing is there would have to be an absurd amount of different combos to account for any possible party configuration...which would be tough to keep balanced. Unless lots of different combinations resulted in the same bonus effect.