Well, you really only need to jack up one front tire and try to turn it to confirm if it is in 4WD or not. If it turns, you have a problem you need to identify.
If the wheel turns and not the CV shaft, you have a PVH issue.
If the wheel turns, the CV shaft and CV shaft on other side turns, you have a PVH issue on the other side.
If the wheel turns, the CV shaft and front drive shaft turn, you have a transfer case issue.
I'd like to know what diagram you are looking at for the chain for the low ratio
I have a BW1354 apart in my shop - its to be a parts donor for my tandem.
Engagement of the front axle, involves the motor turning a shaft with a rotary cam on it, the cam moves the shifter fork, which moves a collar to engaged position (or out). The collar incorporates a spring, so you can shift into position, without everything being exact lined up - then when you move, the difference in rotation will allow shift to complete. This allow the electric motor to complete its movement without concern over stalling and burning out.
The low range engagement is similar.
Now, because the motor has completed its movement, the sensor,
thinks the truck is in 4Hi or Lo (as selected) and lights will come on appropriately, but if the collar's haven't moved, it might not have shifted. On the shift fork, there are a pair of plastic pads which allow for the collar spinning without wear. If your PVH Ranger hasn't been run/put into 4wd/run through deep water/run without oil, it is possible for the collar(s - either/both) to have rusted in place. Alternatively, the plastic pads might be destroyed, and then metal on metal contact (the shift fork is soft aluminum) would mean the collars are never moved into position. Lastly, there is the worn chain which will jump teeth - you probably could make it do that turning a tire, but you would be able to see large amounts of play turning tire e.g. quarter turn forward/back before resistance.