Do the classice investigation method to locate the draw. This means taking the lights out of the trunk and using a VOM to the neg post and neg cable set to the 0.000A scale in amp mode.
Now remove one fuse at a time and see if the reading drops. It should be around 0.040A or less. Once you locate the offending circuit investigate what on that circuit is screwed up. I would sttrongly suggest that you check the trunk wiring post on the left side. Many times these indications you post have been caused by the wiring chaffing and breaking causing shorts, etc.