He watches a giant truck race dangerously through the narrow lanes of the town, and then exchanges a sad shrug with the old lady across the street. His police car is right there, but he doesn't give chase. His relationship with Domino and Joseph is agonizing. Because Joseph is the dominant personality, he enjoys flaunting the law in front of Pharaon, who is so cowed he can't or won't stop him. Joseph speeding and running stop signs, and Pharaon impotently saying that he shouldn't.
Domino listens, neutral.
And a scene where Joseph behaves piggishly to bystanders, and Pharaon is passive. Joseph struts, so that Domino can observe that he is more of a man than Pharaon the cop. Pharaon implodes with self-loathing. The murder investigation continues, sending Pharaon to England and to an insane asylum. His efforts are not really crucial to the solution of the case.