Is this the older car with the old style (69/ earlier) regulator? If so, this sounds more like a sticking regulator (mechanical relay type) rather than a wiring / ground problem.
63 Valiant: the previous owner had updated to Mopar orange box electronic ignition as well as that flatback regulator which almost matches the type in my 1970 Dart. The 70 has plug in type electrical connection where as the one in the 63 has more of an open (wire to bolt) connection. Sorry for the lame description. I'm not sure what type of regulator I should look for. The connection to the wall seems tight but I'll check to see if there are any washers. Thanks