The plug in the back of the shift lever is interchangeable, so it could have been replaced without modifying anything else in the system. The difference between on the fly and not on the fly is the collar of the front axle. If your wheel is spinning and the driveshaft isn't, you won't be able to slide the collar over. That's the only reason you have to stop to shift. The first two pictures show the collar that has to slide over. The transfer case itself did not change at all because that has the capability of meshing and sliding into gear while its spinning. This doesn't happen immediately since it takes several revolutions to line up, but the vacuum motor puts steady pressure on the gear until it happens. The vacuum motor then continues to put a slight pressure to keep it engaged.
If you have a front axle disconnect, you can put a hose clamp on the shift fork and then eliminate the vacuum lines to it. The last picture shows the hose clamp I installed on mine. As long as the collar is in place your axle is ready to go and essentially the same as the solid axle in the "shift on the fly" models.
I also eliminate the shift function on all of my Eagles. The 119 and 129 are both capable of being true all wheel drive. Some people quote a difference in wear and tear and fuel mileage, but realistically there just isn't a noticeable difference. The whole reason I drive an Eagle instead of a Jeep Cherokee is because they are designed to stay in four wheel drive without any adverse effects on the car. It has saved me from serious injury several times. To eliminate the 2WD function remove the vaccum motor and use rope to put a constant and steady pressure on the shift lever. It will pop into neutral and the car won't move if you do not have that steady pressure.