Most Mitsubishi engines are a little noisy, and the 4B11 engines are no exception due to many different factors.
Most of the problems with ticking/rattle noises though are caused by bad fuel selection/leaving oil way too long between changes causing sludge/carbon/other deposits building up/ using the wrong oil for your engine.
If as you said, if it goes away when you switch the engine off then it’s probably engine related, which while narrowing it down still presents a problem to find.
Sounds like the noise is dependent on oil pressure/lubrication, could be timing chain too loose timing chain, possibly the hydraulic tensioner is draining off when parked or there just isn't enough oil pressure due to too much sludge/carbon build up in engine---which is why I asked you in previous posts if the car had regular oil changes and good history, when I say reg oil changes I’m not talking about 15,000++ klm changes either.
There are a number of things you can check, some may sound strange but check them anyway.
· 4B11 Carbon canisters sometimes make a similar noise due to bad design causing the inbuilt valve noise to “be amplified after it starts to wear) similar to valve clicking/rattle noise.
· Air conditioner or idle pulleys
· Noisy injectors (not really likely though)
· Could be a loose timing chain/worn guides--- I’m not sure if the ES/VRX 4B11 or just the 4B11 T/C engine have this, but I assume you have the function/logic monitoring of the amount of elongation of the timing chain which is integrated into the ECM. When the ECM detects the elongation of the timing chain, the warning is shown on the multi-information display of combination meter, looks like a triangle with a ? mark in it from memory, if this ever comes up on your dash, you need to do a visual check of the timing chain.
· I don’t believe that there are any hydraulic lash adjusters on the 4B11 (correct me if I’m wrong) this would make it transmit more noise as well.
· Oil foaming causing problems with inconsistent oil pressure variations.
That’s all I can think of at this time of night, there is more I might think of later, you could try changing oil to 10w/30, fill up tank with 98, whack in a bottle of injector clean and go for a long drive on the highway, see if that helps, other that your mechanic must have a stethoscope, surely he should be able to pinpoint the area or at least narrow it down, unless it’s one of those horrible intermittent faults that magically disappear the moment the mechanic arrives.?