Q: Noise after the car is turned off, car idles rough - 1973 Nissan 240Z

The other day I went to turn the car off and upon turning the key to lock, the starter began working. So, I thought that the ignition switch went bad. I bought a new one and had it replaced. This didn't help however. Also, I've noticed some sound that is similar to an electrical relay that keeps turning on and off every several seconds. It's coming from below the dashboard, in the lower passenger's side. This occurs constantly, both when the ignition is on and off, as well as when the car runs. This keeps draining the battery so I now disconnect the battery terminal to prevent this. The car is idling rough, sounding as if it has no power to remain on when I apply the gas pedal. I had the spark plugs replaced along with the fuel filter, wires, rotor, air filter and distributor cap as well. I checked the coil and it's fine. What might be causing this and how to fix it?