A non-A K-mount lens will normally stop down when not mounted on a body. Moving the aperture lever on the lens will open the iris. When you mount the lens on the body the control lever on the body in the neutral position will push the lever on the lens to open the diaphragm completely. You can confirm this by setting the lens to the smallest aperture while off the body and looking through the front of the lens while mounting it.
Possible causes of an "auto" (with lever) K-mount lens failing to stop down:
- iris covered with oil that has become gummy or viscous.
- lever missing or disconnected
- lever bent or misaligned or jammed
- non-conductive lens mount
Check (1) by seeing if the diaphragm opens and closes rapidly and consistently. You can test this by running through the range of f-stops and watching the opening and closing of the iris through the front of the lens. This can be done off camera by moving the lever manually. If the diaphragm lags or doesn't open fully or stops down inconsistently then most likely there is oil on the blades. The lens appears to work on the MX body but since the test is so simple no reason to be sure.
Since the lens seems to work on the MX we can probably rule out (2). However due to differences of design and manufacturing tolerances the lever can still be (3) bent or misaligned just enough to miss the lever on the K-1 body. Check to see if it is not bent slightly towards the center of the lens (away from the outside of the barrel.
Have you shot a roll of film recently with this lens to confirm it is giving proper exposures consistently?
Ruling out all 1,2, and 3 leaves us with (4). The dull looking finish of the mount in the photos suggests either the mount is oxidized or even non-conductive. That the K-1 asks for a focal length suggests otherwise. Since it a simple procedure to carefully place a bit of metal foil between the lens and camera to cover the "data" pin I don't see any reason not to try it just to rule out non or poor conductivity as a source of the problem. Just so long as you take care not to drop any foil into the mirror box.