It won't run perfectly for long. The coil is hooked up through a ballast resistor and should only get about 6 volts. That resistor could be the problem or an alarm system could be breaking the circuit. It's not the ignition switch because the ECM wouldn't be running and it's not the ECM because the plugs wouldn't be firing. Spring for the Clymers or haynes and you'll get an electrical diagram that will let you trace the coil wire.
Shows you why you shouldn't get advice from Carquest.