1st Gen Tundra Limited Slip Questions

[mattmtbman]

Ok so I have a 2004 Tundra 4x4 Double cab with what seems like a limited slip diff when in 2wd, but when I shift my transfer case into 4x4 the Limited slip seems to disengage. I tested this by jacking up the rear end and spinning one rear tire, in 2wd both tire spin forward then when I shift 4x4 one tire spins forward and one spins backwards. Has anyone else experienced this or figured out a way to make the limited slip work in 4x4?

 

[exploreFL]

I have an 06 double cab, from what I understand that is how toyota designed the diff to operate, engaged when in 4x2 and disengaged while in 4x4.. Weird.... Would be nice if it would stay engaged.