OP, you might possibly have the same issue as I did on my 03 4.6is (same symptoms) and I've also spend a lot of time trying to solve the problem which is quite rare it seems:

In my case it was broken wire in the upper trunk lid in the section where there is rubber boot protecting bunch of wires and over time by opening / closing the lid, mine broke.
I repaired the wire and voila, everything was fine.
I think I posted about this few years back and will try to find the post with more info.

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2010 BMW M6 * Black Saphire Metallic * Full Black Merino Leather
2019 BMW X3 M40i * Alpine White * Mocha Leather