Check the ground strap behind the removable console. Large brown wire/wires ending in an eyelet. This should be attached to one or both of the braces running from the tunnel to the underneath of the dash. The eyelet should be between the brace and the nut. It's not unusual to find someone has removed the brace for some reason and placed the ground/earth eyelet on the outside of the nut. This allows for an intermittent ground because the plastic retainer doesn't hold tight.

Well, it is confirmed, whatever power problem is causing the radio to work only sometimes is also causing the A/C knob from working sometimes. On one of my short trips today, the radio decided to turn on, at which point I tested the A/C knob. Indeed, now when I feel the little click, something responds, a fan changes and the system switches over. So, it was stuck on A/C before, which is why I wasn't getting any heat.

Now, the question is - what would cause both the radio and the A/C knob only (hazards and even lighter both work fine) to work sometimes but not always?