1967 Pontiac GTO cuts-out, backfires-the tailpipes, coughs

With the new electronc ignition, was it installed on a 12 volt line or a 9 volt line. Also is the coil matched to thei ignition? If it's a pertronics I think if you look on the instructions it says to use a 3 ohm coil. If you are using the old coil that may be your problem. Also check the fuel pump for flow, as that may be low as well then make sure the float n the carb doesn't sink in the float bowl as the older carbs tend to do that with today's fuel with alcohol.

Have you checked the vacuum advance, if not make sure everything is free to move with centrifugal force and make sure diaphragm is not busted(it should hold a little vacuum and not leak off). If all this checks out, check to be sure if it has the original timing gears and chain set, they can become stretched, or a little sloppy, about the only way they like to run is with the timing advanced, sometimes a lot. They wont usually run very good set at the factory timing specs. The best way I've found to tune an older engine like this one is to unhook vacuum advance and hook a vacuum gauge in, adjust carb jets +or- 1/4 turn until highest vacuum is reached and slowly advance timing until slight lifter noise is heard(while accelerating)then retard 2 or 3 degrees until no lifter noise at full load acceleration, and then putt around like grandpa on sunday morning and you may get another 150,000 out of it. But you still got to blow it out every once and a while. Ha! I love this model, not many left.