• Which specific auto-splitter script are you using?

I use this one (but this one is used for round speedruns, so it only splits every round). However, I've been messing around with a lot of autosplitters today and I also had trouble getting them to work as well so it might be an issue with BO3 at the moment.

• Are there any specific "Compare Against" settings (Real Time vs. Game Time) I need to toggle for BO3?

You should compare against game time since we use In-Game Time (IGT) as the primary timing method for BO3.

• Common fixes if the script isn't detecting the game process?

Honestly not sure, I've just tried swapping out some autosplitters or running LiveSplit with admin privileges, but I think they just broke.

If you're running an EE run, you can use the Autosplitter and Speedrun mod by cbrnn, which is linked in the resources tab. It comes with an in-game autosplitter, although you can't compare against it. A download link is on the resources tab. Otherwise you'd have to use manual splits, if I find a fix or working autosplitter I'll put in the resources tab but until then you might want to try manual splits or using the BO3 speedrun mod.