It's entirely mechanical except for the solenoid which can be accessed from inside the console. But for the lever to be to the right and the t-case locked at the same time would mean the cable is grossly dis-adjusted. That could bind the solenoid and prevent it from retracting I guess.
I would try to disconnect the cable from the top of the t-case and see if you can turn the mechanism manually. It should be pretty smooth and easy to turn with a small wrench. I can turn mine with my hand. With patience, you can do that from under the truck.
This is the cable on top of the t-case as seen from inside the truck with the center console removed.
(Sorry for the black blob concealing part of the lock lever.)
Inside the t-case, that lever pushes on a spring that in turn pushes on a fork that engages the lock ring. So it can be moved back and forth without engaging or disengaging the lock.
Rotating it about 90 degrees clockwise pushes the lock against the two halves of the differential inside and eventually will lock the t-case when both halves are aligned.
Rotating it 90 degrees counter clockwise will pull back on the spring, and when the mechanical bind is lessened inside the t-case, the lock ring will retract and the t-case will unlock.
So removing the cable on top of the t-case will allow you to do two things :
1- see if the cable moves freely and
2- turn the lever on top of the t-case counterclockwise then drive slowly around to release the bind. If the lock does not release eventually, then there is something wrong inside the t-case.
I would try to disconnect the cable from the top of the t-case and see if you can turn the mechanism manually. It should be pretty smooth and easy to turn with a small wrench. I can turn mine with my hand. With patience, you can do that from under the truck.
This is the cable on top of the t-case as seen from inside the truck with the center console removed.

(Sorry for the black blob concealing part of the lock lever.)
Inside the t-case, that lever pushes on a spring that in turn pushes on a fork that engages the lock ring. So it can be moved back and forth without engaging or disengaging the lock.
Rotating it about 90 degrees clockwise pushes the lock against the two halves of the differential inside and eventually will lock the t-case when both halves are aligned.
Rotating it 90 degrees counter clockwise will pull back on the spring, and when the mechanical bind is lessened inside the t-case, the lock ring will retract and the t-case will unlock.
So removing the cable on top of the t-case will allow you to do two things :
1- see if the cable moves freely and
2- turn the lever on top of the t-case counterclockwise then drive slowly around to release the bind. If the lock does not release eventually, then there is something wrong inside the t-case.