The first time I saw the Suspicious Traveler comes during the mission 'The Killing Moon'. This isn't a mission everybody will play as you only encounter it if you choose the Cyberpunk 2077 Phantom ...

To survive, David becomes an edgerunner, also known as cyberpunk, taking on mercenary jobs outside the system. Together with a group of new and veteran edgerunners, David will shoot for the moon ...

The Killing Moon is also the final mission of this path, though it’s a pretty long, tense, and action-packed finale that leads you into the Cyberpunk 2077 Phantom Liberty Reed choice ending.