a TruTrac is a helical gear or worm gear design limited slip. You should not really notice it at all in 2wd. If you have a TT and the symptoms you describe, you likely have something very bad going on in there.
Remember that a limited slip will never lock up 50/50 like a locker does. Most limited slips will bias torque up to 30/70, and if you have zero resistance on one tire, the limited slip will act like an open carrier. Its the nature of the beast. Apply a little break pressure to ad resistance to the side that is spinning, and it should transfer some torque to the other side of the diff.
And this is even more the case with TruTracs, as Eaton sets the bias differently for front and rear applications. Fronts are less aggressive so they are more 'invisible' on-road.