Mine does, but the transmission mount on the crossmember is loose/bad on mine. I think that's why it does it. It's so loose I can get underneath the Jeep and visibly see that I am moving around the transmission/drivetrain with my hands...
Honestly, i dont think that would be considered normal, at least when new. My Dodge doesnt do it, that transmission/drivetrain is tight in that truck and it uses the same guts (it's a Tourqueflite 999) as the GW's "TorqueCommand" 727.
I'll find out later when I put my Jeep back on the road after the major work I'm doing gets done. I got a new mount and I'm going to put it in during the process. See how it responds afterwords. The whole vehicle should feel tight compared to now with my rusted out frame...
1990 Grand Wagoneer-"The Crapwagon"
AMC 360, TF727, NP229, 3.31gears, 2" lift
Rancho 44044, Rusty's 2" AAL, TFI
...still kinda rusty
1926 Dodge Brothers 5 pass. Business Sedan 212-I4, 3 speed, CRANK START (new long term project)
1987 Lincoln Town Car "Signature Series" 5.0, AOD unknown gears
1987 Dodge Dakota LE 3.9,A999TF,3.90gears(DD)
1994 GMC 'Burban L05-5.7,4L60E,3.73gears(DD)
2001 Jeep Cherokee Sport 4.0,AW4,3.73gears(thinkin of selling)