p.s. i don't think the adobe website, and forums in particular, are easy to navigate, so don't spend a lot of time searching that forum list. do your best and we'll move the post if it helps you get responses.
Sorry for the issue. This issue requires placing "add edits" (razor splices) within the clip where you want to have an effect. That way, you won't have to render any effects you don't need for the clip. Once you have the add edits in place, then drop the effect where you want it, between the splices. You can keyframe or create a mask for the mosaic effect in that region. Let us know if you need help with techniques to achieve what you want. Screenshots can help. Good luck.