Low Idle Problem cant solve

Hi guys,
I just bought a Suzuki Jimny 2000 with an automatic transmisssion and a M13A engine. It has 17500 km on it.
The car has a low idle problem and i cant find the cause of it.
In the morning when i first start the car for the first 3 minuits the car rpm is around 1300. Then it drops to 1000 and suddenly drops again to 500 and stays there, and the cabin is vibrating. It doesnt matter wether it has a gear in or nuetral or parked. It will still do it. Also i have notticed when i turn the steering wheel the rpm will drop and the cabin will vibrate. If i put the A/C on then rpm goes up to 900 and stays there for a while and sometimes it will drop to 500 and then back again. It kind of fixes the problem when the A/C is on but not all the times. On traffic lights, stop signs etc it will do the same.
Now if i drive the car for an hour or so (highway) the the problem dissapears and idle behaves like normal. 800 rpm and no vibrating. I have tested the the car multiple times with this scenarion and after an hour drive it fixes itself. I left the car idling for 20 minuits after that and the rpm stayed constand at 800 and no vibrating.

Things i have done:

1. Changed the trottle body twice.
2. Cleaned EGR valve.
3. New spark plugs.
4. Changed the PCV valve.
5. Serviced the Injections.
6. Cleaned and checked the ignition coils.
7. Cleaned the manifold intake.
8. Changed the spark plugs wires.
9. Changed the valve gasket.
10. No engine light or errors when scanned with a tool.
11. Changed air filters.
12. Checked for vaccum leaks.

I would apreciate any help.
Thank you,

Welcome to the forum. Have you looked at the idle control valve, they can get sticky?

Thank you Lambert.
Idle control valve is part of the throttle body and i have changed that twice the past month.

You appear to have covered all the main culprits.

The start up and interaction with the AC appears normal, so the ECU is listening to all the sensors, this got me thinking.
Is it possible the engine temperature sensor is out of spec and registering low temperature, confusing the ECU? It would explain why long runs etc fix it, it's just getting hotter! Some cars have multiple temp sensor so the gauge temp may be separate to the ECU feed.
Sorry, don't know it this applies to the Jimny, just thinking out loud as they say.

Another (may not apply to Jimny) fault was a power steering sensor that "lifts" the rpm with steering load. Known fault on Ford, the wire falls off the rack and the rpm is low or stalls. Again may not apply.

As you have covered all the main items you are going to look beyond the normal, so just trying to help with some suggestions. If you do track it down please report back.

Mike

Have you check the air sensor in the air filter box? A while ago that sensor was causing the same problem, in my case got solve by that

Were the throttle bodies off known running vehicles or reconditioned, cleaned before installation?