After locking the car I noticed THE REAR LIFTGATE window doesn't lock, the LIFTGATE itself locks but the lift window!! I can just open it . Any help?

I belive that latch has a separate lock solenoid.

See here for the part:

http://www.partswebsite.com/mazdawholesaleparts/?i=1&model=1562&make=136&year=2001&section=141&catid=30195&subcatid=34566&partid=0&type=parts&image=5325550&imagecallout=0