Dashboard odometer lights stay on

If these do not go off after about 5 minutes then they are being kept alive and yes they will drain the battery in about a night.

I suspect this is the body computer has a fault in it and it is keeping the lights on. Then when you open the door that actually triggers the body computer to turn on the courtesy circuit and it will also trigger it to turn these lights off because they are not supposed to be on at that point.

What I would do is check the voltage on one of these circuits coming out of the BCM when these are supposed to be off. So you will need to start the engine and get out like normal when these lights are staying on, then instead of closing the door, just flip the door latch so that the body computer thinks the door is closed but you can actually leave it open in order to do this testing.

Then check the for voltage on the circuit highlighted below and if you have it then you need to replace the Body ECU as all these circuits run through it.

It looks like you can just replace the body computer which is on the back of the junction block. See below for the detail.