Parking Lights on when Turned Off, Starter Keeps Running

[hanks4runner]

This is my first post. My 4Runner has an electrical gremlin that is puzzling. Came home from work, parked, shut car off, turned off all lights, parking lights stayed on. An hour or two later, saw parking lights on, switch was turned off, so I started it and the started motor was running along with the engine, so I turned the ignition switch off and the starter immediately started cranking the engine and would not stop until I unhooked the battery. Hooked the battery back up, parking lights came back on with switch off, but started didn't start cranking the engine. Put in new tail light relay, and the car seemed normal until I went to work next day and parking lights stayed on with switch off, so I once again unhooked battery while at work, and after work got home okay. Replaced tail light relay again, and here's where it got really strange, started the car, and the started motor once again ran with the engine, I turned on light switch and immediately the starter motor quit running and a few moments later I turned the light switch off and the car immediately shut off as if I shut it off, even though the ignition switch was still on...
I assume there is a short in the light switch or ignition switch. Has this happened to anyone else?

 

[hanks4runner]

I forgot to mention I pulled the tail light relay out and everything worked normally. except no parking lights, head lights, brake lights and turn signals work, so it has to be driven in daylight...

 

[nissanh]

Can you find a different relay identical to your parking light relay? Try using it in place of the parking relay. It is most likely a faulty relay.

 

[hanks4runner]

I replaced the tail light relay with a matched one from Advance Auto.
Could a bad tail light relay cause the starter motor to keep running when the engine has started and cut out when lights are turned on and then shut the motor off when lights are turned off, with ignition switch still on?