Electric Ghost in the machine

[Bmwtvboy]

This morning I unlocked the car/security. Then closed the door and locked the security. The left/driver side rear upper tail light stayed on. I open the car, removed the bulb/socket. Closed the car, security set. Moments later I came back to meet the tow truck and the bottom rear left tail light was on. I removed it. The locked and unlocked. Security working. No dash lights.
2 weeks ago the radio wouldn't shut down, the top light/clock bar stayed on.
SO, I removed the radio fuse from the rear fuse links. The security/lock system as worked perfectly. Are these two related? Is this a battery issues to come sign?