8N: that lever on the back is linked directly to the 3-point position lever to allow you to raise or lower the three-point arms from the back, making it easier to attach implements. I don't have the cab model but this is how mine looks:
Now if you lift that rubber flap, you can see the linkages, In this shot the position lever is in the"up" position and you can separate linkages from the cabin position lever and the aft position lever which attach via small ball joints to the lever on the shaft.
Now here's a final shot with the position lever down. Sorry about the sharpness, I guess I moved the camera. The main thing here is the lock screw that is supposed to lock the position lever to the shaft. This is what I'd check. Maybe it's just lose or missing.
Based on your description, the position lever isn't doing anything. So maybe that outboard lever is not turning the shaft. Note that there is a procedure to lock it to the shaft at the proper orientation. If this isn't the case, it's more serious; either the shaft is broken or the other end of the shaft (inside the 3-point hydraulic unit) has come undone. Did you get any sort of warranty?
I would add that a circlip on that shaft keeps the position control arm from sliding off, even if it were lose. Also, there are flats ground into the end of the shaft (beyond the circlip) where you should be able to feel if the shaft is turning with the position control or not.
ADDED Let me also add that the bell-cranks on the shafts don't quite look like the simple "arms" shown in the parts manual or the service manual page posted above. I decided we already have too many things called arms so I'll refer to those draft and position brackets on the shaft as bell-cranks.