Ignition/starting problem

When bypassing the ballast resistor, did you run a wire straight from the + battery post to the + terminal on the coil? If so, it should have fired with the key, especially if a remote starter button would start it. I'd guess that you may not have bypassed the ballast resistor as you may have thought.

When using the ignition switch, the coil is powered by the brown wire coming off the switch which bypasses the ballast resistor. Somewhere along the line that brown wire is broken, has a corroded contact, or what not. Usual suspect is the bulkhead connector. Once you release the ignition switch from start to run, the coil is powered by the blue wire which runs through the ballast resistor. The start button works because you're not using that brown wire circuit, just the run circuit. I may have the brown and blue wires mixed up, plus that's on my '69; not sure the colors for a '63.

You'll need to either find the problem in the start circuit, or just bypass it. I got so sick and tired of mine working and then not working no matter what I did, I just wired a switch to energize the run circuit; all the start position on the ignition switch does is activate the starter. I leave the switch on when I want the motor to run, switch it off when I want it off, like a kill switch.

Could be the ignition switch, but since you've replaced it I'd say it's probably not the problem. My 2 cents and how I fixed mine, I'm sure others may chime in with various tests and so on to pinpoint the exact problem. I just wanted mine to start and run, so I rigged up what worked without worrying about originality or looks.