Toyota Repair: Toyota dies after 10 to 20 minutes, electrical leakage, electrical problem

Question
Hello Ted, My son has a 1988 corolla with a 4 AF engine.  I installed a new short block and everything worked fine for awhile.  After about 200 miles, (maybe two weeks) it began to sputter and lose power, I felt the problem might be fuel delivery so I rebuilt the carburetor this,  seemed to remedy the problem.   About a week later he was driving and the engine died and would not restart after about an hour he was able to get it started and drove home.  The next time I drove it for about 20 minutes everything was fine, the following day it died after about 10 minutes, again when it sat for awhile it restarted. I could not check the trouble codes because the check engine light never comes on, even with the key on and the engine not started.  Hopefully you can give me some help in finding where the problem lies so I can get it fixed.  Thank you and I apologize for being so long winded.

Answer
It seems like an electrical problem, there have been issues with distributors on these engines, check the coil inside the distributor for cracks, remove the cap and rotor and the coil cover and check the coil, look on the top for cracks and any signs of electrical leakage on the underside of the coil.