Idle Shake - Splutter and engine out :(

[IG38]

Hi guys.

I was just wondering if there was anyone out there who might have an insight into a Yaris issue that has been bedevilling me for the last few weeks.

My '07 Automatic Yaris is experiencing the following symptoms:
- revs drop to about 500 at the lights;
- whole car / engine bay shakes;

Sometimes, the engine will rev itself back to about 1k rpm, and then settle back normally. Sometimes, I shift into neutral, and just gently rev to 1k just to keep the shakes at bay.

The moment I get the green light, the car is off and running (lately I have noticed the car is a bit more sluggish after the shakes, but usually comes back online strong after a few seconds of running)

I've had the throttle body cleaned, the MAF sensor cleaned.

Car has always been dealer serviced. When the issue first manifested, I brought it back to the dealership. Was told nothing on the computer.

However, I'm putting this urgent reach out because the previous shakes episode ended with the car cutting out. I was able to restart, only for a second shake episode that not only cut out the engine, but made the brake pedal stiff - couldn't stop the car rolling (I had moved quickly to N to restart at the lights) and used the parking brake to stop. My dealer service is booked - but in a weeks time (couldn't fit me in earlier).

Does anyone have any insight into this issue? Would appreciate it someone could point me in the right direction (or at least give me a broad area to point the mechanics to look at)

Much thanks in advance
Ian