So the lamp stays lit with in not attached to the housing? If so try unplugging the two wires at the transfer case one at a time and check. My 70 Fj40 the switch was crumbling apart and lamp never lit. One of those wires should be grounded and the other goes to the outside of the lamp socket...
The lamp on the dash has a plastic isolator between the housing and the lamp socket. Lamp socket plugged directly into the housing gives the lamp a ground that suppose to come from the switch on the transfer case.