I'm going to assume that the below image is similar to your car.
2003 Honda Civic Classic Pictures/Photos Gallery - The Car Connection
A newer Honda undergoing wind tunnel testing:
Honda Factory News - Acura TSX Forum
Combining the two (I could not find the proper image) we get:
Aerodynamics Photos by kach22i | Photobucket
[URL=http://s184.photobucket.com/user/kach22i/media/Aerodynamics/honda-overlay_zps56b8eb8c.jpg.html]
Based on viewing maybe a hundred wind tunnel images, I'm going to guess that detachment on your car occurs about 2/3rds of the way down the rear glass.
This air flow then jumps over to the top of the truck lid without too much turbulence, and goes on to provide a tiny bit of down-force.
My suggestion is to focus on the rear deck lid and rear sides, cant inward at about 10 degrees with some attachments, minding not to obscure your brake lights.
Think 3D
Honda Worldwide | March 29, 2007 "Honda Adds New Type R to Civic Lineup"
