Engine quits

An engine needs three things to run, mechanical integrity (which it must have or it would not restart), fuel and spark. To find an intermittent problem like this ( I work on a lot of Toyotas, I "tee into" the fuel line and tape a fuel pressure gauge to the windscreen so I can monitor fuel pressure when the problem occurs, if fuel pressure falls off you then start tracing the fuel pump, fuel pump relay and sensors that allow fuel operation. I also drive around with a timing light attached to one of the spark plug wires, when the vehicle falters I pull the trigger on the timing light and see if I have spark if not I check the ignition system and wiring and sensors associated with the ignition system. Intermittent problems are hard to find and your vehicle has limited diagnostic capabilities. Understanding how each system works, having a good wiring diagram and volt/ohm meter and patience are required to trouble shoot this kind of problem.