Electrical nightmare

I have a 1969 Dodge Dart custom, with a
360 CI motor topped with a Holley 4412 500 CFM carb and a 727 torqueflite trans. My problem is car runs for a short period Of time and then backfires through the exhaust and dies but will refire after a short. time the only thing that I've recently changed it the ignition switch what could the cause of the problem be?
Thank you to all who replied. Here is the update. I have points ignition so i started with those and condensor, that didnt fix it so i went with coil, plugs, wires and cap. One of those 4 fixed the problem. With further inspection i found my coil to have been leaking oil which i assume was to cool it and caused it to overheat and fail.