Interesting! If I remember right the new Mustang trunks seem to collect water as they slope down toward the back window, but just before getting to the edge it slopes back up leaving a nice place for water and the like to collect... hmmm this would make a good place for dirt and whatnot to collect causing the look.
This is definitely a bad design. I clean the area every time I was my car which is at least twice a month but it's too a point that it's starting to permanently stain. Luckily it's hidden but still bugs me. Not sure what Ford was thinking when they designed the trunk. I'll snap a photo tomorrow if I remember.
Interesting thought about the car wash causing the brown spots. When I first got the car I thought it was specs of brown paint. I do occasionally use a touchless Lazer wash by my house. Helps keep the crud down in between washes and no scratchy brushes. Might have to rethink that now if that's what's causing the brown specs. I'm curious if there OP had his from the same culprit.