Going off of the earlier commander's theory about Nysa: I did run into something similar to what he had said. I went through the system with a fine tooth comb after instancing around 25 times and never seeing a ship named Child. For the record, you cannot follow an NPC if they drop at a station. Whether you head to the station yourself or follow their low wake, they will not be there. I believe the commander was reading far too much into the NPC vanishing as it is simply how things work in the game at the moment.
So, fine tooth comb. The system has a Coriolis station, an outpost, a handful of surface outposts, and two dockable surface settlements. Two of these outposts have data points which you can scan, so I figured I would play detective and go snoop around. While both messages received were basically nonsense, upon leaving the second planet I heard a notification for a mission objective. Lo and behold, as the commander said, there was in fact a random mission signal about 500kLs out from the system. I headed there and found a wreck with some food canisters, water, and a black box. The moment I scooped the black box, I was given offered an assassination mission. An assassination with no text from Nysa Brotherhood. Huh, never had that happen before, but, alright. Its suggested rating was Elite. Sorry Ben Wilson, but this guy says your time is up and I'm 10 miles down the rabbit hole. The entire time I'm chasing him down, he's saying things like "Please, I just want to be left alone." "I just wanted to help people." "Please don't do this." But, he's wanted....hm...again, weird....but, the rabbit hole says you gotta die. Did the doormouse say anything about murder? Chase him down, kapow-kablooey, dead Ben Wilson. Head back to Nysa, turn in my mission...nothing. Reputation change. No new interesting missions. Snoop around the outpost, nothing notable on the outside or around it. No notable characters floating around. I sit in Nysa for 20 minutes, relog, jump out and back in, visit a planet and leave, all the while I never get another random mission.
So...I'd love if anyone here could go and try to replicate this, and see if they find something I didn't. Good luck commanders. For the record, my Ben was in an imperial eagle and a somewhat decent fight against my heavily engineered Cobra.
The Demeter Ritual says initiates must not have blood on their hands so maybe you should let the person escape and abandon the mission or let the timer run out.