3DCG Generalist and Animator Tsubasa Suzuki recently shared a time-saving workflow they sometimes use to animate jiggle and sway.
It involves creating multiple looping secondary-motion animations on animation layers based on overlap, adjusting the overall direction and position on the base layer, and tweaking weights of animation layers to prevent the motion from feeling obviously repetitive.
The drawback here, as the artist notes, is that since overlap is the base, refining the silhouette becomes very difficult. Watch this video by Lee, also known as leedoppo, and check out their fantastic animations: