DON'T MODIFY THE TUBES!
Sorry for shouting!
Is the mount of the extension tube, where it mates with the lens mount of the camera body, chrome (bare metal) or anodized ("painted" black)?
If it is anodized, try this: put a piece of aluminum foil between the Vivitar AT-22 tube and the camera, where the electrical contacts on the lens mount are.
If that fixes the problem, you've just confirmed that the anodized surface (electrically insulating) is the cause of the problem. The contacts on the lens mount of the camera has to be grounded for the camera to actuate the aperture lever of the lens). To fix the problem permanently, you can use sandpaper to scrape off the tube to bare metal.
The photo below shows you where to scrape. The issue with the extension tube (actually a de-glassed TC) in the photo is different from the problem you currently have because it has electrical contacts.
Older Pentax DSLRs (K20D and older) do not have this issue.