It sounds like Tim, 52Carl, Mike , and Whitedog have given you great information to work with.
I am a little curious though, you indicated that you have a 12V Generator, and 12V solenoid operated starter with a push button starter system.
It sounds like you do not have a ballast resistor to drop the 12V to 6V for your original stock distributor which uses points ? Maybe I missed something and you have a 12V HEI system. If so, ignore the rest of my post because its not relevant.
Where I'm going with this is on 12V conversions there is usually a ballast resistor. The wire from the ignition switch (on) goes to the ballast resistor, wire from other side of ballast resistor goes to the + side of the coil. An additional wire is ran from the S terminal on the starter solenoid to the + side of the coil. The S terminal enables a full 12V to go to the coil when initially starting the motor and provides additional spark for starting. Once the starter disengages ( you let off the button ) the S terminal is disconnected and the supplied voltage drops back to the normal reduced voltage from the ballast resistor to the coil.
I was looking for areas in which to consider wiring issues.
Please let us know what you find as knowledge is power and every learning experience helps.