1991 Camry not running after hot and turned off (solution) what I learned.
 

First off, the 1991 seemed to be a year that not a lot of information exists on line. From 1992 on, there is all kinds of info on the Web.
I was having trouble with this 1991 having ana periodic dead keyrkey for 5 minutes, running fine, but dying, or running and driving fine, but when you turned the car off to go to the store, you'd return, start the vehicle and the car would run bad and die.
If you waited for the engine to cool, or overnight, you could start the car and it would run and drive normally and get the car back home.
i changed the fuel filter, no change in behavior.
The codes read that the ECM was bad. I changed out the ICM, (which is just to the left of the battery). I changed the ECM (which is behind the ash tray), no change.
Finally, I changed out the distributor which houses the internal coil and this seems to have fixed the issue. When I changed the distributor, I also replaced the valve cover gasket. NOTE: I would recommend replacing the valve cover gasket at the same time as replacing the distributor, as you can see the internal distributor connection and guide the finger of the distributor into place. It is so much easier this way and will save you tons of frustration. You likely need a new valve cover gasket anyway and getting the cover off is not difficult. The valve cover gasket nuts torque inward to out at 17ft lbs.

I have tested and driven the car 5 times. Each time getting her hot and turning her off, letting her sit for 5 or 10 minutes and starting and driving the car again. It seems at this point, problem is resolved.

I learned a lot of lessons from this. I should have just replaced the distributor first since this was likely a coil issue and the coil is inside of the distributor.

GP

Thanks for posting. Your info will help others.

UPDATE:. I have driven the car for two days, climbing into the mountains to work and back. All is good. Car is running great.