No response seems... not great. But Yukio isn't lashing out at him or throwing up again, so it could probably be worse.

Ginko just stays where he is for a while, one hand resting stationary on Yukio's back while he waits to see if he seems to be recovering. He doesn't speak for a while, either, giving him a little more time and silence. There's probably more he should do here, something to comfort him or make things easier, but Ginko can't imagine what. Rubbing his back like he's a sick baby doesn't seem like it would be particularly helpful, and he can't imagine that trying to follow up Yukio's silence with verbal comfort would end in anything but disaster.

So he waits, and when he does speak again, his voice is still quiet and careful. "How are you feeling?"