Check the POLARITY of the voltage at the coil with a good DMM with the key ON and the key OFF but with the lights on. I suspect that the polarity will be reversed and the voltage relatively low with the key off but the lights on.
Ignition off, lights off 0.0V Ignition on, lights off +12.1V Ignition on, lights on, +11.9V Ignition off, lights on, +10.9V
68' Firebird 400 convertible, numbers matching, solar red w/ deluxe parchment interior. 66' Pontiac Ventura Hardtop 66' Pontiac Catalina Convertible