There is some weird mojo going on with those rear hatch circuits. In my previous 80, I managed to track down taps that gave me switchable lighting under the hatch.
It always had power. After several hours of poking around on the new LX, sorry, no bueno.
This may be because the right hand rear door circuit did not cause that courtesy light to come one when the hatch was raised, just the left side one. I didn't bother chasing that down. However, after giving up on the alternatives, I did find as connector that plugs into the rear hatch locking mechanism. It yielded a reliable 12 V with the hatch opened to light things up, but whenever I tried tapping into it with my lighting by means of those plastic Scotchlock-type connectors, again, no bueno. Seems whatever was going on either with the circuit to the right rear door light or the lock itself - turning the key in it just unlocked the hatch and did not affect anything else (although locking the locks from other locations did lock and unlock the hatch.)
So I disconnected this connector from the lead to the hatch lock, then hooked up the lighting and a switch tucked away behind the hatch grab handle to it. Works! But only so long as the motor isn't running. Not a problem as I don't anticipate using those lights except when the motor is off.
Interestingly, the hatch lock still follows the central control faithfully still. I don't see any extra wiring that could explian this, but happy that it does. I alos noticed the left courtesy light no longer responds to the rear hatch's open/shut status, although like the right still function when the related door opens and shuts. That also is fine with me, as these always required the carabiner-in-the-latch trick to shut off when sleeping in there with the rear hatch open.
This solved that problem. Anyway now got nice hatch lights, but not sure exactly how.
I do have the EWD (for the old 80 series, anyway) and can usually make sense of it. Didn't really help much with the rear hatch, except for wire colors/connector pin outs.