The vehicle in question is a 2007 Chevy Silverado 1500 LT extended cab, 150k miles on the clock. A picture is worth 1000 words, so here's 2000 words about the problem:
It's a very wet day here in New England which is why everything is wet and has leaves stuck to it.
The question is how to fix this? Is there a kind of double stick tape that would actually last? Is it something I would glue on? I don't even know how to approach this in a way that lasts and isn't ugly.