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Print page 5126-02 to 04 at
http://www.e38.org/e32/e32_88_etm.pdf
Notice that there are 2 motors inside the 4 Door Lock Motors M12 - 14, and only 1 motor inside the trunk and fuel flap lock motors M16 and M17.
The extra motor, driven by the BLK wire at pin 1 of the lock motor connectors, is the actual Deadlock function. It sets a pawl that prevents the other motor from unlocking the door. It is supposed to be Deadlocked by the alarm system, and then Deadlock-Released 30 minutes later, or when a key-holder unlocks the passenger door.
It is a beastly thing. I recommend cutting the pin 1 BLK wires, so the Deadlock can never trigger again.
Perhaps your rear door locks got a Deadlock pulse, and never received a Deadlock-Release pulse. This is strange because all 4 door motors share the same BLK Deadlock wire. Of course the front doors are privileged because they have key locks, which the rear doors lack. Perhaps the Battery was weak when the last Deadlock-Release pulse was sent, and the rear doors did not fully execute this command.
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Please print pg 5126-00 to 05 at
http://www.e38.org/e32/e32_90_etm.pdf.
On pg 03 you see flags G,H,I for wires BLK, WHT, BLU.
On pg 02 you see that the relays inside the RM are shorting all 3 wires to GND. So if you power BLU and WHT wires with the RM installed, you will just be feeding a short circuit.
So, remove the RM. Now the 3 wires BLK, WHT, BLU are floating and you can do what you want with them. It is convenient to work with the wires at the trunk lock motor (except BLK is not there.).
If you connect 12V to BLK and briefly GND the BLU wire then all 4 Deadlock motors (4 doors) will Deadlock.
If you connect 12V to BLU and briefly GND the BLK wire then all 4 Deadlock motors (4 doors) will Un-Deadlock.
If you connect 12V to BLU and briefly GND the WHT wire (with BLK floating) then all 6 lock motors (4 doors, trunk, fuel flap) will Unlock (say).
If you connect 12V to WHT and briefly GND the BLU wire, then all 6 lock motors will Lock (say).
It takes a lot of current to power the locks.
If this does not work then you need to find and fix the short / open wires. Then, knowing that the Output Details are OK, you can look at the Input Details - switches, etc.
I hope this helps.
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The BLACK wire is for the DEADLOCK motors, and it is not our friend.