The detection rule 'GitHub User Initial Access to Private Repo' identifies instances where a user first accesses a private repository within a GitHub organization. This rule is triggered by actions that involve the audit log from GitHub, specifically monitoring the activity when a user performs a push to a repository that is not publicly accessible. The logic is built around checking the presence or absence of the user in a set of previously recorded access entries, thereby effectively distinguishing between initial access or repeated actions by the same user. The rule includes tests for various scenarios including an initial access attempt, a repetition of access which should not trigger the rule, and attempts to access public repositories which are excluded from this detection.