Well,

After thinking I'd just ignore the problem, I was in the garage an heard the hatch whirring (not an accurate adjective) away as if the switch was pressed. When I took a look, it had 'released' and the trunk light was on. Obviously, not as easy to ignore a switch that thinks it's being pressed as a switch that doesn't work.

So I took it apart and the assembly was very wet and grimy. The gasket that seals the switch / handle / license plate lights assembly to the tailgate as shrunk and rotted, and allowed a lot of water in. The mechanism looked okay, and I think my problem was corrosion / bad connection at the electrical connector. I've cleaned it up and will see if it is temporarily fixed, while I order this gasket..

Gasket, trunk lid grip
This fits your 2000 BMW X5 3.0i
Part Number: 51137004531

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2000/12 BMW X5 3.0L
1989/12 BMW 325ic
2000 BMW E39 528i