You should service both the advance rod and the pivot posts on the advance unit that the weights rotate on. If you've never done it before, it's best to take the weights off the posts, clean the posts, clean the holes in the weights, lightly grease both, and re-assemble. There should be a thin wave shim washer behind each weight on the post so take care not to lose that. In the future, you can re-lube the pivot posts without taking things apart again using a little foaming chain lube. Do it after a ride while the motor's still warm/hot so it penetrates better. This can all be done without removing the advance unit from the bike.
The advance rod can be serviced as well without pulling the advance unit off. Just remove the little disc in the center that connects the ends of the weights to the rod. Then you can pull the rod out from the points side, points cam still installed. Clean the bushings in the cam, pack with fresh grease, lightly grease the entire length of the rod, and re-install.