I may have missed something, but isn't this what he says if told to stay ?"staying in Kaer Morhen" doesn't mean "living there forever". He would still go out on the Path, but come back during the Winter. If you don't convince him to, he'll say that he's never coming back, period, due to the sadness that the old fortress brings him.
And this is what he says otherwise:Geralt: Come on. It's the only home we've ever had. Stay.
Eskel: No, Geralt. Place has been dying a while. Last nail in the coffin today. Time we accepted that.
In any case, ignoring this particular choice would not be a major issue, he could easily change his mind either way, or end up having to leave for other reasons. From the conversation it looks like he always leaves, but it does not exclude the possibility that he may return occasionally later.Geralt: I get you.
Eskel: Try my luck in Lormark. There's always work where there's war. After that, we'll see.
Geralt: Till next time.
Eskel: See you, Wolf.