4wd circuit

Have a 1990 Chevy 4x4. Seems like the 4x4 circuit is a bit messed up. My 4x4 light on the floor is on at all times, even when I am in 2wd. Pulling the 4wd fuse kills the light. Unplugging the 2nd set of wires down by the actuator kills the light. If I shift into 4x4, I still get 4wd even with the 2nd set of wires unplugged (the ones that don't go into the end of the actuator). Seems to me that whatever switch in the actuator completes that circuit is stuck on. Is anything else affected if I leave this 2nd set of wires unplugged? Do I need to get a new actuator to eventually fix this issue? Thanks.

Update: Replaced the actuator, no change in behavior. I suspect the switch at the T-Case. Anyone ever tried to diagnose a problem with this switch, or can let me know how difficult it is to get to/change one out?