This was a few versions back, but I also played Tywin in the Robert's Rebellion scenario. I'm not sure if I sided with Robert or declared my own independence, but I went to war with the Targaryens and got an event where Jaime killed Aerys and left the Kingsguard to come back to me, which was pretty cool. I don't even think the event is Jaime-specific, it's just based on what Jamie did in canon and has a chance to happen whenever a Kingsguard knight has a conflict of interest.