Alright I've figured out what's going on with the Killer module. There's a few problems with having the PC as the killer.
Normally the PC can't be forced to perform any interactions via trigger. You can usually get around this problem by first enabling Auto PC mode. For some reason though the game won't allow the PC to perform a murder interaction even in Auto PC mode, and instead the character will just perform the Nevermind interaction. The module instead tries to get around this issue by switching the PC before having the original PC do the murder.
This leads to another problem. The game ends if the PC is killed, so if the module were to make the victim the PC, the game would end right after the murder and you'd be kicked back out to the main menu. So instead the module tries to find a 3rd character that it can make the PC before orchestrating the murder that is neither the original PC, nor the victim. Unfortunately, if the module is unable to find a 3rd character to make the PC, then the rest of the module fails to work as intended, and the murder never happens.
TLDR: The module only functions properly if there's at least 3 characters in the class.