> This isn't quite accurate either. You can stay as a tourist
Unfortunately you're not accurate either.
What you're referring to (staying as a tourist) is the same 3 month limit I was talking about. An EU national can come to Switzerland for up to 3 months without doing anything special at all. After 3 months, you can apply for a short-term visa to search for work for a further 3 months [0] or you can apply for residence without gainful employment [1].