The Investigator is a construct of the Protomolecule, where it uses an edited version of Detective Miller's persona, to look into the disappearance of the Protomolecule's parent race. The Investigator interacts with James Holden through the Protomolecule's manipulation of Holden's brain; in which he essentially hallucinates the Investigator.
Abandons Gate (SPOLERS)
At some point The Protomolocule decides allocate resourses to the replication of Miller, who was a talented detective and could furthers the Protomolocule search for the Ring Gate Builders
The Investigator, first appears to Holden at the end of Caliban's War after The Ring Gate has made it to its location past Neptune's Orbit. The Investigator, taking the form of Miller, mysteriously warns Holden about Doors and Corners. Three Days later Holden finds out about The Ring Gate getting breached by a rogue belter who uses Gravity pulls off planets to gain the required speed to make it out to The Ring Gate.
Initially, The Investigator shows himself to Holden in a confusing state where he makes little sense, non sequitur phrases which do nothing but scare Holden into believing he is getting manipulated by the Protomolocule. This is further exacerbated by the Blind Camera man giving a photo of Clarissa Mao who is mistaken for Julie Mao.
The first clairvoyant conversation between Holden and The Investigator happens when Holden makes his approach, alone to the Ring Station. Still confused as to where the Investigator comes from and why he is there, Holden asks why he is being framed by Julie Mao. The Investigator replies "She's dead kid, I don't want to talk about it". The Investigator also explains that he was unaware of appearing to Holden before in a more confused state, stating that it "scares the shit of him". The Investigator later explains that when he becomes powerful within the protomolocule construct, it will kill him, and he is reborn within the construct, he says "he's good at dying".
After arriving on the Ring Station, The Investigator opens up the pathways in the Ring Station. Once Holden arrives in the room with the console, that only physical entities like Holden can approach and not the Investigator. After seeing the recap of the end of the Civilization that was the Ring Gate Builders, The Investigator explains he can shut down the Ring Station's security protocols if Holden can get the fleet of ships to lower its power out put enough.
Once the Fleet and finally the Behemoth shut down there reactors, The Investigator shows Holden one of the planets on the other side of the gates, while in the hallucination which seems quite real to Holden The Investigator explains there is a habitable planet on the side of every gate.
It is soon revealed the The Investigator permanently shut down the dampening field affecting the speed of the ships in the slow zone, while also opening up the unopened gates. This is potentially the second time Miller saved the Sol System.
The Investigator explains to Holden the he wants to continue to explore and see what really happened to the Ring Gate Builders.
Cibola Burn (SPOILERS)
Due to events not related to the Protomolocule, the crew of the Rocinante make there way to Ilus to help mediate an issue with the RCE colonists and the Belter Squatters. When the Rocinante's crew arrive, with Holden and his Miller Ghost, they unknowingly cause the planets Ring Gate Builder assets to begin to wake up. In space this causes the ship reactors to shut down, forcing them to rely on battery power. On the planet, they first see nearly broken Protomolocule Scarab Robots that have be activated but are succumbing to there age , then the reactors deep under the sea that have been inactive for billions of years, blow up, causing a massive planet wide storm that forces the people at New Landing to retreat, hastily, to the near by towers built billions of years earlier.
While this all happens, The Investigator insists that Holden go to a Crater, that is hundreds of miles away, to investigate what is in the crater because he can't see within its depths unlike the rest of the planet.
After finding a cure for the Green Blindness, Holden, who has been defending the camp from death slugs, passes out in a sleeping bag after a multiple day bender. In his sleep, the Investigator insists that Holden go deeper into the tower and enter its planet wide transit network. After a little cajoling, Holden makes his way to the Transit Network, where he passes out.
After a long trip to the mysterious crater Holden is side tracked in his attempt to enter the crater and shut down the weapon inside, by Murtry who has made his way up to the crater in a land vehicle. Eventually Holden finds Elvi, who he gives the task of shutting down the weapon with the Investigator/ Miller Bot.
After some instruction on where to go from Elvi, The Investigator/Miller Bot starts the shutdown process of the Protomolocule Network on Ilus. He explains that anything that is part of the Protomolocule Race will instantly die if it enters the circle in the middle of the room. Soon local defenses come to try and stop The Investigator/Miller Bot and Elvi. While Elvi successful in not dying the The Investigator/Miller Bot is severely wounded and is forced unhinge its self from Miller Bot, eventually showing that inside the Miller Bot is a heavy oblong shaped egg creature. The Investigator asks Elvi to pick up the heavy egg and place it within circle, essential destroying it and all the Protomolocule assets he can find and destroys him self.
While not said directly, his sacrifice could of been made to end the suffering of the hundreds of thousands of people who died on Eros but lived on because of the Protomolocule.
Holden, after returning to the orbit of Ilus, decides to look through the area where the Protomolocule Hybrid was digging into the ship, and finds a pollup the size of a fingertip. This part of the Protomolocule had been how the Protomolocule always seemed to follow Holden.
The Investigators primary mission was to search for Ring Gate Builders. The investigator was largely indifferent into the survival of the human race, other than Holden who needs as a conduit for searching but will only help Holden if it helps his own means. The Investigator explains he chose Holden because Miller liked him.