I am assuming that the thought that I am intelligent enough or over the past 50 years of owning and working on cars have accumulated enough knowledge to know what "an accessory kicking in" might look like is beyond your abilities.
If my assumption about your abilities is incorrect then please explain to all of us why this phenomenon only appears if the vehicle is in park or neutral? Is there some special accessory that only kicks in when in park or neutral and when in drive or reverse does not kick in and therefore the idle is rock solid?
Please feel free to elaborate on your description of this special accessory.
Here is a visual aid to assist in you explanation ...
Be sure to explain why the idle will be at 750 RPM, then slowly drop to 500 RPM, then quickly accelerate to slightly less than 1000 RPM and then slowly drop back to 750 RPM. This 10 - 15 second cycle will repeat over and over until you shut the car off.
A 500 RPM variance is one hell of an accessory kicking on and off, and it does not do it abruptly like an air conditioner compressor clutch but rather "oozes" from each RPM to the next.
Note that when the air conditioning compressor clutch engages and disengages there is a noticeable click, a minor change in RPM and it happens no matter what position the gear selector is in, and will happen even if the air conditioner is turned off if the heater controls are in any of the windshield defogging positions. I became familiar with this phenomenon in my first air conditioned car ... a new 1973 Pontiac Grand Prix.
Given that I have owned cars for over 50 years I believe I can answer 'Have you guys driven literally any other car?" in the affirmative. Given that I have never had a car that exhibited this type of idle I find the FR-S behavior strange. Examples of cars that I have recently driven that do not exhibit this behavior includes the new Camry I used while they had the FR-S in for diagnosis, the wife's Yaris, either of my MR-2's, our Toyota truck, the neighbors Toyota truck, the other neighbors Dodge Ram, the son-in-laws Ford truck, ... but that is only in the last 6 month.
Anxiously awaiting your explanation ...