Your car is charging, right? Put a multimeter set to volts across the battery. With the car running, you should see about 14V.
First I'd make sure that the trunk light is indeed off. Maybe the switch that controls that light is bad. I've seen this once and you don't usually notice it, since the trunk is closed.
Set the multimeter to current. Put it in series with the rest of the car by disconnecting the red battery lead and tying the + of the meter to the battery + (perhaps get a spare battery connector so you can do this conceniently or have someone hold the wires together) and the - to the red battery lead. Don't start the car or turn anything on as this willblow the fuse internal to the multimeter. You should see a minimal current drain -- a couple of milli Amps.
If you see significant current drain, pull one fuse at a time to isolate what draws this amount of current.
Also, if you've drained your battery down several times it will significantly decrease the life of the battery. It may look ok, but don't exclude the possibility of having a bad battery if you don't see any current drain. It could still be that.
Let us know how you make out.
Hope this is useful. Remco