I thought mine was faulty but then released it was me that was "broken"...
If you have your remote key set for two presses to unlock all doors, the trunk will only be unlocked on the second press of the key with all the the rest of the doors. So unless you unlock the car fully (two presses) the trunk will not open from the trunk switch/button but will from the key or internal release.
Your probably well aware of this and I don't mean to insult your intelligence but wanted to make certain you aware of this before starting to poke and prod the car with a multi-meter.
An e39 is like a beautiful wife, needs constant attention, lots of money, lets you down at the worse times but you’d never be without it.