Possessed tail lights draining battery

Bought a old 2002 Impala with 93K miles at auction about 2 years ago. Police edition, 3.8L. Everything was fine until about a year ago;

1)the taillights start coming on at random when the car is off. Sometimes they are full on, sometimes just soft glow, but it kills the battery overnight. Have been just disconnecting when not in use, wipes the time on the clock but otherwise no problem, aside from the inconvenience. Initially thought it was brakelight switch or DRL, but both seem okay.

2)A few months ago, the turn signals started acting up - randomly won't work for a few minutes now and then. Also getting a check engine code (mechanic told me it was oxygen sensor).

The police supplement booklet to the owners manual states that they do some custom programming, such as disabling the automatic interior lights when the door is opened, and adding a button that kills all lights while running, so I'm already thinking it's all electrical.

Online forums suggest replacing the BCM and/or ignition switch as the solution to most problems - does this sound like a possible fix? Any input much appreciated.