Check for codes for sure. You can clear them by pulling the EFI fuse. If they come back they are real. There is a diagnosis procedure in the Supra factory manual or Cygnus x1 web site.
http://www.cygnusx1.net/Supra/Librar....aspx?S=EM&P=4
It could be many things. Check that EGR valve is functioning with the car off by running a hose down to the vacuum diaphragm and apply a vacuum by mouth then release it. You should hear clicking sound when released and the vacuum should hold when you pull one. Doing this a few times could also bust up any carbon chunks that might be allowing gases to bleed by causing your rough idle. In fact the manual test of the EGR valve is to do the same thing with the engine running at idle which will stall the engine. One time a throttle position sensor was sticking internally and I didn't find that out until I took it off and noticed that it wouldn't come back to the idle position against the metal tabs on the throttle body side. There is a test procedure for the throttle position sensor that involves using a dial ohm meter and feeler gauges. Make sure the airflow sensor is plugged in. Check for vacuum leaks in hoses and splits in the larger rubber connectors. Check the engine spark timing and if necessary the valve timing / timing belt. Check the 02 sensor function using the manual procedure with a dial voltmeter. Idle mixture is established using the idle air valve which has a stepping motor in it. The test procedure is described in the manual. You can test the ignition coils if you want to. Follow the procedure. You can also test the ignitor as well. Look for a loose or disconnected vacuum hoses. The hose diagram should be under the hood. There's a T connection and behind the intake manifold on the firewall make sure that hasn't come loose. if the the heater is working then it's not disconnected. Make sure the spark plug wires go to the proper places. For turbo car of the firing order left to right on the coil pack is: 1-5-3-6-2-4. Spark plug gap for a Turbo is 0.032" for a non-Turbo 0.043". Look for cracked plug insulators. I always use a flex joint on top of the socket. Torque Plugs to 16 ft/lbs. Looking at the spark plugs can tell you about the state of the engine cylinder by cylinder. You can also run a compression check. Make sure the air filter is not plugged up / dirty. A through system check should narrow the cause down.