Technically the remnants of Garlean influence left in Eorzea or no longer a large government, they're a rogue agency. Gaius lost support from the motherland when political issues arose in the courts back in Garlemald so he's acting entirely on his own now, which would make them a large military force but not a large government. If you're going to pick and choose your clients in that way then you're not really true neutral, you still have a moral ground you're standing on. If you wanted to be truly neutral mercenaries you'd work for anyone, anywhere, doing anything so long as they could pay you.
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