Need to first identify the transmission and the T-Case. You are correct the t-case shifter isn't supposed to move. On a stock YJ it actually is bolted to the trans.
89YJ 2.5L TBI, AX-5, NP231 SYE, Ford 8.8, Yukon Grizzly, Tom Woods Shaft, 33" BFG T/As, 4" lift, Warn VR10000s.
AF Jeep Club Tail #184