I realized that I forgot to write how I learned to actually double-expose on purpose with the Pentax K1000.

As I had written this morning, there is no one button that will cause the camera not to forward a frame while allowing you to trigger the shutter.

Instead, you have to hold the film-rewind button, then you forward the frame with the winder lever. I read somewhere that you are advised to 'waste' the next frame into the lens cap because the frame forward spacing might not be correct and you could be making an accidental triple exposure on top of your planned double-exposure.

Once again:

1. Take the first exposure
2. Press in the film-rewind button at the bottom of the K1000
3. With the film-rewind button still pressed, forward the frame with the winder lever as you would to go to the next frame.

   The winder should cock the shutter release but not pull the film forward. Instead, it will stay on the current frame.

4. Fire the second exposure
5. Wind to the next frame as normal without holding the film-rewind button

Update: and what the manual says

The manual confirms the above instruction but first advise that you take up the film slack with the rewind control first and then follow the steps outlined above.

Update: not much success yet

Not sure how I did this wrong but I have one good double-exposure but then it happened to creep onto the next frame! Interesting juxtaposition and nearly random art.