The eligibility period of a former servicemember consists of: the weeks in the former servicemember’s benefit year that begin during the additional benefit period; and if the former servicemember’s benefit year ends during the additional benefit period, any week thereafter that begins during the additional benefit period. To be eligible for additional benefits for a week during an eligibility period, a former servicemember: shall be unemployed for the week for which benefits are claimed; shall meet each requirement of this title for regular benefits that applies to a claim for additional benefits; may not be subject to disqualification from receiving regular benefits; and shall have exhausted all UCX benefits to which the former servicemember is entitled.