Since practically every hollow space within an 8/7/5 is host to a control unit, many with memory and sensors, it is no wonder the E31/32/34 has such a high resting current drain. About 1 amp/hour drain about every 20 hours. Here's the figures:
With the trunk/luggage compartment lights off:
1.) Driver's door open: 4.8 - 5.0 Amps
2.) Driver's door closed: 4.1 Amps for 20 seconds then reduced to approx. 450-470mA for next 16 mins. then reduced to approx. 50mA
With the trunk/luggage compartment lights on:
1.) Driver's door open approx. 6.1-6.4 Amps
2.) Driver's door closed--approx. 5.9-6.1 Amps for 20 seconds, then reduced to approx. 2.5 Amps for the next 16 mins, then reduced to approx. 50mA
Hope that helps when searching.
But that all does not drain your battery completely.
Paul's idea might go into the right direction, as this is a known cause of problems.
Check the cables at the the trunk hinge wiring. For sure you will find something.
The unlocking also could be a problem of a defective microswitch in the doors and the trunk.
You can also install a multimeter between the battery and the battery cable and the pull fuse after fuse till it drain drops. By this method you can allocate the area where you have to look for.
Also check lights/switches in glovebox, trunk etc.