2009 Suzuki Swift RS415 auto (not sold in USA)

Hi folks.  My grandson has the above car here in Australia.  It has an intermittent rough idling issue.  I'm new to electronics but have done some testing and replaced some parts (mea culpa, mea maxima culpa) without fixing or changing it, but my latest efforts in diagnosing the cause has pin-pointed the Idle Air Control Valve.  I had the engine running with the front half on the airbox off after replacing the spark plugs. This was fortuitous as it allowed me to hear the change in air intake sound when the engine was idling fine then misfiring. It was obvious that the Idle Air Control valve was activating and deactivating, causing a distinctly different sound. I put a scope on the middle wire on the IAC plug and saw it spike when misfiring and relatively stable when not. If the revs are held at about 1500, all is well.  the first link below is if the change in air intake sound, the other is of the small scope I connected to the middle wire of the IAC valve.

I should add that this rough idling is very intermittent.  On a half hour stop/start drive say, it may happen more often than not when stopped, another time it may happen just a couple of times.  The engine has only stalled twice at a stop and restarts immediately.  The car runs perfectly under all conditions except for this intermittent idle issue.

drive.google.com/file/d/197K45O1MkU_C1XwSL_JmAJcSNJe6xZp7/view

drive.google.com/file/d/1UFhtrZ9JzFI9YJkrw6BasTeibABy8FkN/view

You can hear the rad fan/air con coming on and off repeatedly at idle in the second clip, but at 1500-2000rpm it behaves normally - which seems to suggest that it's getting a wrong message too. What do you make of the scope spike and on/off fan-air con noise?

Where to from here?  TIA.

Here's a page from the FSM.  Is the ECU at fault???
 
 

More info - no DTC have shown up; the EGR valve has been removed checked electrically, visually and operationally - all in spec.  The car has done 360,000km (216,000m) and has been serviced regularly since new (by me   ).

Here's the ECM chart -
 
 

On delving deeper into the FSM I've discovered a 10 step procedure for testing the IAC valve, wiring and circuits.  I guess that'll be my next activity when I can get back to the car - which is 300 miles from me.     

Wow, that thing has some serious miles on it! I don't think our Suzuki cars lasted that long.
I don't know that I have any real direction for you yet.
What parts have you replaced? Just tune up stuff like plugs and wires or more?
Does this car have a MAF or MAP or both?
I'm thinking the IAC may possibly be cycling up to keep the car running. If you haven't yet, it probably wouldn't hurt to clean the throttle body and IAC passages.
Does anything stand out in live data like changes in fuel trim?

Thanks for the reply Noah.  

The coils & leads were replaced about 20,000m ago - this issue started about 5 months ago, well after that.  The plugs have just been replaced. 
What parts have you replaced?  I'm too embarrassed to say     O well here's the list:  just the IAC valve and the crank position sensor.  The EGR valve has been removed, tested electrically and visually then refitted.  

Does this car have a MAF or MAP or both?  Yes, both in the one unit located just before the TB.  The TB has been cleaned.  

Does anything stand out in live data like changes in fuel trim?  I'm at day 2 as a scope learner, so I don't know how to check that - yet.

This page shows what the waveform of the IAC should look like at No.19 but I don't yet know how to correctly set the scope to read properly.  
 

When I can get back to the car I'll do the 10 step test - which says the ECU could be the cause, as a last resort.