The initial access achieved by cyber adversaries conducting a systematic attack against a targeted network is unlikely to be an asset of interest. Therefore, it is necessary to use lateral movement techniques to expand access to different devices within the network to accomplish the strategic attack’s objectives. The pivot attack technique is widely used in this context; the attacker creates an indirect communication tunnel with the target and uses traffic forwarding methods to send and receive commands. Recognising and classifying this technique in large corporate networks is a complex task, due to the number of different events and traffic generated. In this paper, we present a pivot attack classification criteria based on perceived indicators of attack (IoA) to identify the level of connectivity achieved by the adversary. Additionally, an automatic pivot classifier algorithm is proposed to include a classification attribute to introduce a novel capability for the APIVADS pivot attack detection scheme. The new algorithm includes an attribute to differentiate between types of pivot attacks and contribute to the threat intelligence capabilities regarding the adversary modus operandi. To the best of our knowledge, this is the first academic peer-reviewed study providing a pivot attack classification criteria.