The plastic surrounding the third brake light in the rear window rattles like crazy with certain bass frequencies. I can stop the rattling if I apply upwards pressure on the cover. I tried stuffing some thin felt strips between the roof liner and plastic housing but it had no effect. I'm wondering if there are any creative ideas out there to control the rattling.

Ideally I would like some sort of removable plastic, rubberized or silicone solution to apply along the edges of the plastic housing. I was thinking about a thin line of caulk but I'm worried about permanently damaging the plastic, and I'm not the best at caulking anyway.