2015 Siera Denali 2500 Duramax - Interior Instrument/Control Switch Backlighting Stays On 24/7

[CFee]

For several months now my 2015 Siera Denali 2500 Duramax batteries go flat after 2-4 days sitting.  I just installed two new GM Gold batteries.  An obvious problem is that the backlighting on various interior controls, including: Red lighting around the headlight switch and drive more selector; lighting for trailer brake controls; dimmer switch light; lighting for passenger and driver reading light switches, also rear seat reading light switches; and lastly, piano key (aux switches?) switch lighting.  See the attached photo of the drive mode selector and trailer brake controls.  Photo was taken after the truck hadn't been driven for 24 hours - red backlighting and white control illumination should NOT be on. But they and all the others are.

 

What I've done:  

1. Removed all the fuses from the driver side dash panel fuse block: lights stay on.  

2. Disconnected the bulkhead connector from that fuse block: lights go OFF. BUT: after manually turning the headlights on - the backlights ALL go on again, then fade out slowly (like they are supposed to)when I turn off the headlights.

3. Disconnected all the wiring going to the K9 BCM controller (behind the OBD port). Lights stay on.

4. Put the truck in Transport Mode.  Lights stay on. 

5. Took the truck to a large nearby GMC dealer  They charged me $228, replaced a fuse for the Trailer Brake Controller, and told me I needed two new batteries before they could go any further.    (I bought two new batteries at a much lower cost and installed myself.)  I am hesitant to return to that dealer...

 

The truck has only 79,000 miles.  Any suggestions?  

 

Edited 3 hours ago by CFee
adding info