So I'm running my campaign still and curious, would a pirate born eldar object to getting his hands dirty? I mean like physical labor for instance manually mining out ores on a planet, as part of a mercenary party who couldn't find a combat mission to take.

I'd say yes. He's an Eldar and a pirate, so a noble pirate. He's not going to do anything that isn't explicitly involved in pirating, but what he does he'll do it perfectly.

Self-preservation instinct transcends species, so I'd say if there is no other option to get by, he'd certainly rather do this than starve. However, I'm sure there are other options -- and rather than Eldar, I'd say more defining is the fact that the character is a mercenary. He'd rather turn to piracy than become a dirty miner.

More to the point: I assume this mercenary company has a means of interstellar transportation, so why aren't they just going elsewhere? In a setting such as 40k, there must be someone willing to pay for a couple more warriors.

the mercenary company is more or less beginners, like we all decided:"Hey, we know how to use a gun, let's go fight!" the party is currently 7 members strong" and the only place that had a lot of combat currently we left due to it being overrun by orks and Chaos, 8 Mercenaries who are equipped with low rank stuff isn't going to kill a bunch of Orks who just overran a settlement the only one onworld.

and the hive world we fled from had a Daemon prince claim it as his, his new world is currently under siege by the local Imperial fleet.

and we paid some rogue trader to get us out of the sector.

Our own ship is just void capable and this sector we are in more or less a frontier sector.

Though there is some trouble in the sector it won't pop up until a little further in

Oh, I see. I admit, that's not necessarily a group I'd see an Eldar hang out with, but I'm just going to assume he or she has some tragic background about just how they'd have gone from being born to Eldar pirates, to ending up in a rag-tag band of wannabe-mercs. And in that case, I suppose the Eldar may already be miserable enough to agree to such unsuitable labour if it's the only way to bring food to the table.

Still, are there no better jobs? What about using their ship to offer passenger travel? Or simply stealing ?

Owning a void-capable spaceship (whose cost would be measured in hundreds of thousands, if not millions of Thrones), yet only being 8 people with low-grade weapons and, or so it appears, no savings is a strange combination.

Can't you pull a Han Solo and take a loan with the ship as collateral, provided you don't wish to simply sell it? Could lead to some interesting complications or even a new nemesis later on if you still can't pay ...

the ship is barely void capable, we got it as a bargain i roll to see if it gets a leak every so often or not, and it's armed with Two sets of Twin-Linked Heavy Stubbers.

we practically stole it ish, + I don't think Power Armour would be 15K if it was to be totally lore friendly to be honest, not to mention I don't think it would be available to everyone.

I had some players ask if we can use the warp I recently told them no, as warp and void are different

An Eldar could totally be a miner...

VERY different. Imperial warp engines have to be huge to function more or less safely, which is partly why Imperial warp-ships are kilometer+ long behemoths. And truth be told, I imagine this Eldar would be a lot more opposed to traveling the Warp without a Gellar field (or even with a human Gellar field) than he is to getting all Exodite-like and actually (sniff) working.

Historically, though, groups of well-armed, dangerous, unemployed and soon-to-be hungry people tended to go for banditry or extortion rather than poorly paid unskilled labor.