Yaris idle vibration

[Japcars9]

I have a petrol yaris. It would be the slight facelift model 2010 1.33 6 speed. It comes with stop start in this year.

I have changed spark plugs, oil, air and cleaned cam and maf sensor including throttle. Further to a drive belt change.

At 51000 miles what could be causing this slight vibration on idle. It doesn't seem to affect engine revs. Just the cabin shakes a little.

I have also noticed the stop start doesn't work. Despite reaching optimum temperature. The Battery is about 6 months old from toyota directly. Fuses all working 

[FROSTYBALLS]

There are a number of factors that determine whether the stop/start system works - not just whether the engine has reached optimum temperature. 

[Madasafish]

If you do only short journeys , it may be carbonned up and need an Italian Tune up..(Lots of driving at high revs).

The throttle body may need to be cleaned.

The engine mountings may be weak (check gearbox one as well).