some tips
on older points type cars. leaving the key in the run position and IF the points were closed it could start overheating the coil. The bad ground is probably the problem, there are two circuits in a coil , the primary and secondary windings both have to have a good ground to work., on a points car the primary ground was thru the points, the secondary (spark ) circuit was thru the case, With a bad ground that circuit tries to ground somewhere else, put a feed back current where it shouldn't go. a bad condensor used to also cause problems. When the spark occurs that collapsing magnetic field induces a current in the primary windings, that then puts a small amound of voltage back into the secondary, that would repeat until it died down, It only took a milisecond, On an osciloscope you would see the wiggles tapering down after the spark patern. There could be a bad component inside the ignition module. Does it have a good ground. ?