This is a 2009 1.8 Corolla with 150k km on the 2ZR-FE engine. At idle RPM's cycle up and down by one or two hundred RPM and there is a gasping or rotational noise from the right hand (belt) side of the engine. The noise seems to cycle on and off around every second there's a short video here, it's a hard to hear but the RPM can be seen changing.
I run a smoke test on the intake with no leaks, the PCV valve is clean & rattles nicely, the intake manifold gasket is good. There are no check engine codes otherwise the car drives nicely at all speeds. I don't think this model has an intake air control valve as the throttle is drive by wire. Long term fuel trim's 0%, the short term moves around a couple percent positive and negative.
EDIT 2019/06/05 MAF sensor cleaned, injectors all have the same resistance, problem remains
EDIT 2019/06/06 Brake booster vacuum check valve tested with no problems, ran idle relearn by turning key a couple of times before starting. At the moment the noise is most present in drive or park whilst idling at traffic lights with the engine fully hot.
EDIT 2019/06/11 Ordered a new water pump to replace the original which may be causing the noise described, will report back in a couple of weeks. Regarding the RPM fluctuation one friend thought this was a faulty gauge on the instrument cluster.
EDIT 2019/06/23 changed out the water pump and gasket, no change to the symptoms
EDIT 2019/06/24 Seems the fluctuation and noise could be separate. A local mechanic thought the gauge movement was an instrumentation problem. Of course the engine didn't make the intermittent noise at that time. We managed to grab a another recording of the noise.