When is a river formally determined eligible or ineligible?

Eligibility findings are made as a part of a congressionally authorized study under Section 5(a), or pursuant to agency inventory and planning under Section 5(d)(1).  For Section 2(a)(ii) rivers, the National Park Service will make an eligibility determination under authority delegated by the Secretary of the Interior following application by the governor(s) for federal designation.

Source
Interagency Wild & Scenic Rivers Council