Klaus does have a route. You want some help finding it?
here! (copypasted from rickalick)
1. Get a coat on day 1(either talk to Rune before losing the key, or ask Devon for help when you lost it)
2. Do the Klaus event when given chance on the first day. Make sure you talk to him and follow him all the way into the woods.
3. After that follow...
3.a) the Bjorn route, in which case just wait till you get a chance to chase after Klaus into the woods again.
3.b) the Devon route, in which case don't help him with telescopes and talk to Klaus in the cafeteria.