This may work a bit better when there is a larger group started up. But one idea is "choice" events, or ones specifically designed to cater to light or dark side options. This would help mesh with the light/dark side point system that was discussed.
The idea that first came up as a simple event. While on a field trip for padawans, an unexpectedly large creature burst through the forest/setting/exc. The children got out safely due to the efforts of the teacher, but there were injuries involved, and the beast is obviously predatory with little fear of us. The larger problem being it saw where the class escaped to/can follow their trail and can attack the base at any time. Judging by its size and strength, if it got to the temple there would be lots of damage, as well as the younger generations in danger of collateral injury.
The choice part comes into play now as there is two mindsets forming. One side who wants to just kill it and be rid of it. The others wish to pacify it and/or send it elsewhere. Though it would be difficult, and comes with a risk of it returning someday, it is still a creature of the force and is not evil. Just acting on instinct. If a large enough group is divided enough, just this event would create an interesting fight where one side is trying to kill the beast, the other side trying to hold them off and influence the beast with the force....and the beast trying its best to partake in the buffet that has come to meet it.
Feel free to leave a comment or thoughts, and as well any ideas you might have for an event with the possibility for two sides forming wishing to solve the problem in multiple ways, using both sides of the force.