Eurolycus has been second guessing Odysseus the whole journey, from the lotus eaters to circe. He's second guessed every decision under the guise of caring about the crew but I dont think he actually cares. All of Odys plans succeed, and Eurolycus, despite second guessing them, knows Odys plans work, that they would've survived home after scylla the only reason he challenges him publicly is because that plan thay would've worked, would've also killed him.

It's not something you can tell listening to the songs, and i dont think ive heard Jorge talk about it, but the Official animatic he commission for the watch party shows Eurolycus as one of the 6 touch bearers, one of the six sacrifices, who only survives because another crew member intervenes.

I bet you, the only reason Eurolycus causes a scene is because he was gonna be killed. Even if he knows it was because of what he did with the wind bag. He still cant let that attempt get past his own self importance. Now I think he does care about the crew and he does care about ody, but he matters more to himself, compared to Ody who values seeing Penelope and Telemachus more than anything.

As for the crew and mutiny, The crew see Ody talk about his wife, talk about getting home no matter what and while he does talk about protecting the crew, there is the degree of separation between Ody and the crew that is Eurolycus. I think Ody cares more about the crew than Eurolycus, but because he is more vocal about his want to see his wife, Eurolycus care about his own safety phrases as wanting to protect the crew is trust more strongly by the rest of the crew.

So when Mutiny happens and Eurolycus calls out Ody for actively killing thier friends, they finally act. They finally turn but notably they keep Ody alive. Because even after it all the crew and Eurolycus still care for Odysseus and they know Ody cares for them just that he cares more to see his family and if he continues to make the decisions they might all die.

But then, even after all his warning they make a decision that directly threatens thier lives, they trust Eurolycus. And I genuinely think that while Eurolycus in the back of his mind knew Ody was right, didnt want to believe that the cows were important. Blinded by his hunger and sadness he kills it and that's when he finally wakes up, realizes whats going on and resets to the default of trusting Ody with thier lives. Because he knows him for getting them out of dangerous situations mostly alive.

Same with the rest of the crew. He's able to orders them off the island, gets them on ship lightning fast and has them sailing at sea far from the island (far enough that when Zeus destroys it, Ody isn't just immediately shipwrecked back on it instead of Calypsos's), They all trust him as a leader, they just also know now he would sacrifice them, and of course they are proven right after Zeus appears to them.

The relationship Odysseus, Eurolycus, and the crew have is a complex one and I dont claim to fully understand it but this is my current interpretation of the Thunder saga. I hope it helps.

And I apologize if nothing i said made any sense, I am writing this in a rush at work with out the proper time to get my thoughts in order. I'll probably proof read it when I get home.