Corporate 8.25 Rear Axle is a corporate Chrysler OPEN differential and yours is a 3.73 Rear Axle Ratio, not a limited slip Trac-lock according to your build sheet!
The rear differential operation has no connection with the operational mode selected on the transfer case!
Automatic single brake operation to enhance traction did not start until the 2006 models.

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Supporting Vendor and Moderator of LOST05 Jeep Liberty CRD Limited 
Ironman Springs/Bilstein/Shocks
Yeti StgIV Hot Tune
Week's BatteryTray
No FCV/EGR
Samcos/ProVent
SunCoast/Transgo
Carter Intank-pmp
2mic.Sec.Fuel Filter
Flowmaster/NO CAT
V6Airbox/noVH
GM11 Bld.fan/HDClutch
IronrockArms/wwdieselMount98 Dodge Cummins 24 Valve