A couple of thoughts on this strange item
I agree with with Dave on the strap mounting arrangement, it looks suspiciously like the K98 grenade launcher sight band so I can only assume it was mounted to something with a diameter roughly of a K98 just to the rear of the rear sight where the grenade launcher sight is mounted. If it did mount like the grenade launcher sight, it would sit off to the left side when sighting the rifle, making the adjustment knobs accessible with the left hand and still allowing the left hand to grasp the stock when firing.
There does not appear to be a rear ocular opening so an illumination device of some sort comes to mind.
There are fins to act as a heat sink at the rear so whatever light or electronic source at the rear would have to be producing some heat to warrant this arrangement.
The mount adjusting screws adjust the tube in two directions but are a bit coarse and do not have a locking mechanism so I don't think it was intended as an accurate sight by any stretch but they do allow aiming of the device.
It would be interesting to know what kind of plug may have been on the end of the electrical cable that might give a hint if it plugged into a battery box similar to the sights used on the MG series optics.
Looking in Darrin Weavers book there is an illuminator that was built by Agfa (bzz) for the G/K43's that could would act as a flashlight with a trigger mechanism that slid onto the scope rail. Could this be a similar solution for the K98? A prototype perhaps?
The plastic or bakelite knob looks suspiciously like an on-off switch. Does it rotate like one?
If the knurled ring around the tube rotates, this may be a beam width adjustment.
If you are feeling like digging deeper, see if there is a way to open it up at the rear to see if it is a simple light bulb socket or an electronic device. This would give further hints as to the purpose. Look for any markings or stamps as well.
I love a mystery