1996 Chevy Corsica Engine Cuts out erratically, seems to be

I have had an on-going problem that is very strange for quite some time. Last year the engine would start to cut out erratically after driving for a while. It would increase in frequency to the point that the engine cuts off and the car will no longer start. If I wait a few hours, the car starts fine and runs again. Strangely, this only happens when the outside temperature is >100 degrees. So, this problem has only happened during the summer. To make matters even wierder, even after the car cuts out completely, the speedometer, temp and fuel gauge will also spasm erratically and the check engine light also flickers erratically with the key in the ON position, even when the car is not running, However, No other electrical components do this. The dome lights, headlights and Radio stay on normally. All other dash indicators like oil, battery and seatbelt lights stay on solidly, no flickering.

Engine code said it was the Ignition control module. I have since replaced the Ignition control module and ignition switch and the problem persists.

Further, during the times that the car does not start. If I put the key in the ON position (but not turning the car over). I do not hear the humming sound of the relay priming the fuel pump. However, after waiting a few hours, when I try to start it again, the relay starts up and the car turns on. I have also replace the relay and fuel pump.

I've taken the car to a mechanic for diagnosis, but they couldn't find the cause.

Can anyone help? Thanks