Look on the side just below the fuel pressure regulator and just to the left side of the IAC to see if the cap for the idle stop screw has been removed. It may be that it's been tampered with since you're finding so many other things the OP 'tweaked'.
Cap had been removed, so I figured, how much more damage can I do if I screw with the screw? LOL
I tried resetting the IAC valve using the procedures I found on PFF and in the manual.
But after taking it out of diagnostic mode with the IAC unplugged, the engine will not start, so I cannot adjust the idle air screw. Is this an indication of a bad IAC?
If I plug the IAC back in, engine starts, but of course with the symptoms again once it runs warm.
And yes, I disconnected the battery, reconnected it, drove for about 60 KM at 35 mph and more, with stop & go and full stops with engine off in between.
That Karmann Ghia is looking better and better!