I was going to suggest the cv joint at the front of the rear diff - they get dry and the ball bearings move a lot when the load changes direction. I've seen that issue on an e39 touring but it sounded much more like marbles in a tin can than your single clink sound.

Some folk have managed to lube the cv without removing it...

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Wayne
2005 BMW X5 3.0d (b 02/05)
2001 BMW F650GS Dakar (b 06/01)