Veterans' Second Amendment Rights Restoration Act of 2018 This bill sets forth procedures and conditions for the adjudication of veterans as mentally incompetent. Specifically, the bill requires the federal government to prove by clear and convincing evidence that a person is a danger to himself, herself, or others in order for a person to be adjudicated as mentally defective. Veterans must be provided certain notice, including written notice of the effect the ruling may have on their ability to own and possess firearms. For an administrative competency proceeding to be initiated, the Department of Veterans Affairs (VA) must first determine (1) that a veteran requires the assignment of a fiduciary due to a finding of mental incompetency, and (2) the VA has a reasonable basis that the person may be a danger to himself, herself, or others.