My 2009 Camry is doing the same thing, I put new motor mounts on, loosened them and re-tightened them and also cleaned the throttle body. Still have vibration coming from the engine. I have been told the throttle computer has to relearn the idle, I tried to disconnect the battery for an hour and it didn't work. When I am at a red light, my rpm is 700. I can press the gas pedal to 1000 and the vibration goes away. Is there something like the computer that controls the idle under load. I need more help from the public thanks if anyone can help.
The slightly high idle and roughness at idle sounds like a symptom of a vacuum leak in the intake system. It also would cause it to go away when the throttle is slightly depressed taking the engine off idle (~1000RPM)
Here is how you can test that theory: A common trick I used in the shop is to spray the intake area from the throttle body to the cylinder head including vacuum hoses with carburetor cleaner or other combustible spray. If the intake is indeed leaking and ingests the combustible vapor, the air/fuel ratio will richen back up and smooth the idle for a second or so. I have also used propane from a small plumbers torch for the same technique. This is slightly on the dangerous side to use these combustibles on an operating and hot engine so do so at your own risk. You may also be able to hear a leak "hissing" or "whistling" if you use a section of hose against your ear and move it along areas of the intake and associated vacuum hoses while the engine is running.