Look for the wire that is to the coil from the ignition switch. You should find a ballast resistor in line with the coil. And it is probably open. With the starter engaged there is 12 Volts on the coil and it will start. With the switch in "run" the voltage will be about 9 Volts at the coil. Sounds like it stops at the ballast resistor. It is a simple fix and the resistor is cheap too. Here is a picture. Don't worry about the text for Pertronix, the picture has a red circle around the Resistor.
https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRw&url=http%3A%2F%2F67-72chevytrucks.com%2Fvboard%2Fshowthread.php%3Ft%3D450680&ei=VLNhVOeoEI35yQTh_4DQDg&bvm=bv.79189006,d.aWw&psig=AFQjCNHg5JVCKc9xfwSlmX74642LyiHS1A&ust=1415775406587322


Steve H