I imagine that an Eldar corsair, much like an Imperial rogue trader or Drukhari archon, would surround herself with a motley entourage, including people from other races who happen to have useful skills or who simply strike her fancy for various reasons. Perhaps also some exotic pets from all over the galaxy, many of them dangerous. The Court of the Archon models provide a good starting point.
Corsairs are likely rather decadent, loving to flaunt their wealth. And since they are masters on their own ships, they can afford to behave in ways that more disciplined factions might find unseemly, such as commanding their crew in combat while languidly lounging on their dais and getting a pedicure.
You could ask around your local gaming community for spare bits, such as Space Marine helmets, Tyranid heads or various weapons, to make piles of loot and trophies.
All in all, I think that in many ways, corsairs lean more Drukhari than Asuryani. Not sadistic, but extravagant, individualistic and self-indulgent, caring nothing for the ascetic discipline and grim sense of duty of their Craftworld-dwelling brethren.
EDIT: Oh hey, look at that, Warhammer Community just posted
an article on a corsair army. It's more about modeling and painting than fluff, but it can still provide inspiration.
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