If its a plug that may have had a switch on the end at some point from a previous owner they only way it would affect the running is if it was for fuel cut off or one of these switches which cause you’re exhaust to backfire and “shoot flames” or in anyway follows back to the ignition or fuel system. I’m guessing you mean near the key barrel ignition, if it is unplugged and isn't touching anything or shorting against anything then it wouldn’t cause a vehicle to run rough, is there any lights on the dash? does the plug have power to it if you use a multimeter?