Detailing - cleaning glass around the brakelight shroud

Every time I get to the inside of my rear window I cringe. I can never get down far enough into the groove where the brakelight shroud meets the glass to remove the residue. From the outside, you can see the dirt around it and it drives me nuts! MOst people would never know it was there to look at it but it bugs me. Any suggestions?

Long wooden sppon or brush with wet paper towel of index or seomthing.