Cliff #87 here.

Regarding the alarm, I think I've noticed that having a really low battery voltage will set it off. So getting it on a charger that at least holds system voltage at 13+V will eliminate that as a possible cause of the alarm, also making it more fun to find the actual problem.

Beyond that, in case you are not aware, these cars go into a "sleep mode" 16 minutes after key out and doors closed (locked too?). So if you measure a high current, and wait long enough, you may notice it dropping after 16 minutes.

And yes, pulling fuses while monitoring current (clamp meter would be best for this) would be a pretty safe and quick way to isolate the problem. You'd want to trick the trunk, door, and hood-open sensors into thinking they are all closed of course.

Good luck.

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2001 X5 3.0i, 203k miles, AT, owned since 2014