1995 Ford Mustang Wont Shut Off

I just recently bought a 1995 Ford Mustang V6 convertible with a 5-speed manual trans. They ignition cylinder was always a little bit touchy, but just today it started up fine, but wouldn’t turn off. I can start it up, but I have to stall the engine to turn it off. It will run with the key out even. I read online that it might be the ignition cylinder or a broken plastic piece that goes between the ignition cylinder and the ignition switch. I’ve tried a completely new ignition cylinder and taken the covers off the steering column only to find the plastic piece is not broken. The car still wont shut off correctly. I have found that the car “dings” with the ignition cylinder is in (meaning the driver’s door is open) and everything else works (windows, top, etc) even without the ignition cylinder. I take this to mean that the car is normally in the “on” position and the ignition cylinder simply cuts the circuit in order to shut the car off. Can anyone tell me what might be wrong, how to fix it, or how the entire system works?