I have a 1988 W124 TE with about 200k miles on it.
One thing that I have tried to figure out for a while now is the rpm at idle.

It only happens sometimes. Other times RPM sits normal at about 600.

Here is the situation. Sometimes when I start the car, the RPM will go up to 1500 in P and stay there. When I change gears to R or D, the RPM will immediately go down to 600-800.

It happens when I am ready to park after driving too. If I switch to P, the RPM will go up to 1500.

I noticed that it usually happens on my way back home, meaning not the first start in the morning.

Any ideas? I will add if I think of anything else.
I may post a video too.