RPM jump-rumble and near stall outs

[Caretaker]

I have brand new Denso plugs in my 2009 Corolla Vibe. I also have a brand new alternator, brand new battery, and have had the induction system cleaned. Here's the problem:

RPM flutter: especially when coming to a full stop and even more so when it is a hard stop. The RPMs go down to about 650 for a split second making the car feel like it is going to stall. It then corrects up to the 750 level for proper sitting idle. This does not happen when the A/C is on since the idle normally stays a bit higher than the 750 resting idle. Also, when the A/C IS ON, I notice the RPM needle jumping back and forth when my foot is off the gas and travelling at around 35 MPH. The range when the needle jumps around is between 1200 and 1400. In this case, it could be a matter of the tranny downshifting causing the RPMs to be jumpy in this worthless 4 speed automatic transmission.

I have no check engine lights so there are no stored codes that I'm aware of.
At 88,000 miles, I have NOT had the PCV valve nor the air intake gasket replaced since it is a very complicated procedure (thanks Toyota), and I left the original ignition coils alone when I changed the spark plugs. The coils did not look burnt so I did not pay the money to switch them out. This has been going on for at least 3 years. So over to you experts: is there an idle control valve on these Corolla engines, or something else you can point me to which would make the RPMs jump or plunge in the case of coming to full stops?

[vibrologist]

Since '05 they are DBW (drive by wire) and the idle is regulated by the PCM.
The things I would do before blaming either the DBW or the PCM are these: clean the throttle body, check the throttle position sensor(I think it has one) and check for vacuum leaks.
I would also disconnect and reconnect all the wiring harnesses to make sure any minor corrosion in the contacts are removed.

[Caretaker]

Thanks for taking the time Vibrologist. Let me add this: the drop of RPMs while coming to a full stop can easily be simulated:

With a fully warm engine, idling with foot on the brake, lower the driver's window all the way. Let go of the power button. Now, once again, depress the power window button to lower the window even though it is all the way down. Does everyone get a drop of RPMs from 750 to close to 600 causing the engine to rumble as if it wants to stall? That is the sensation I get when my engine is fully warmed up and I come to a full stop with the air conditioning OFF. I don't get this drop of RPMs every time I come to a stop, but probably about 1/3 of the time. Is this normal?

[lannvouivre]

Thanks for taking the time Vibrologist. Let me add this: the drop of RPMs while coming to a full stop can easily be simulated:

With a fully warm engine, idling with foot on the brake, lower the driver's window all the way. Let go of the power button. Now, once again, depress the power window button to lower the window even though it is all the way down. Does everyone get a drop of RPMs from 750 to close to 600 causing the engine to rumble as if it wants to stall? That is the sensation I get when my engine is fully warmed up and I come to a full stop with the air conditioning OFF. I don't get this drop of RPMs every time I come to a stop, but probably about 1/3 of the time. Is this normal?

I think it's because it's taking up slack. Try raising or lowering all the windows at once and it should have to work even harder. See if you can actually get it to stall!

I would go ahead and clean the TB, as that's simple and can solve similar issues in Toyotas!