I think you have a leaky reflector/license plate assembly, both my Mystiques had that problem until spending an afternoon regasketing with foam tape and Strip-calk, sold at body supply shops or Advance Auto parts. The clue is the back up lights will have rust on the metal contacts, and the bulb socket may need to be cleaned and silicone greased. Water will drip out of them when the trunk is open. You might have to open the access covers (mine were gone). It may work to silicone caulk the top edge of the reflector where it meets the metal, if you are good at caulking. Removing the lens is a pain but the best way to fix it, I can provide a procedure if you need it.
