Dome & interior lights staying on too long

This has been a problem for some time -- but seems to have gotten worse lately. Thanks in advance for any ideas for a fix.

In sequence of events, leading to current one.

- For past 3 years, my "door open" dash warning light has been remaining illuminated, despite all doors and rear hatch being closed. Researched the issue here, and determined was probably a door sensor. Tried to fix myself using approaches suggested (cleaning/lube door latches, graphite, etc), didn't work. Dealer wanted $500 to find/fix sensors -- so i decided to live with the light. Past 3 years doing this.

- About a year ago, the interior lights started staying on much longer than usual -- after parking and turning off the vehicle. Usually it takes 10-15 minutes before they turn off. This is still how they're behaving.

- A month ago, I replaced both batteries in the vehicle, with high quality replacements.

Now...the current issue and my question to the experts here...

- Last week, I went to drive the vehicle, which had been sitting in the driveway for over a week, and battery (main) was dead. Recharged, and vehicle started right up.

- During this drive after charging, I noticed that my interior lights are now STAYING LIT WHILE DRIVING. They do not shut off. However, when I stop and shut off the vehicle, the interior lights do shut off...after their "normal" 10-15 minutes of staying on...as they have for the past couple of years.

One of my acquaintences has suggested that ALL of this might be the "BCM" (body control module)? I have no idea what that is.

Any help from the experts here much appreciated.

By the way -- I love my '03 6.0 Excursion 4x4 --despite these quirks.

I2D