This MIGHT resolve your problem but the E53 corrosion is only ONE issue. The other is that the plastic stand-offs melt over time. There is a BMW Service Bulletin fix on this (S.I. B63 08 07) involving a specific Henkel made adhesive / filler (can't recall the name) - it's posted on the outpost.

I had removed corrosion and built up the terminals with solder - that was OK for nearly a year.

You need to do BOTH for a permanent fix. I applied this myself (I used epoxy putty in lieu of the Henkel product) to my tail lights. Do this proactively.

Removal of the tail lights (10 mm socket) works well with a tiny ratchet and a good light to see. My car doesn't have any CD changer, amp or similar in left storage cubby - so much more room.

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2002 Euro X5 (E53) 3.0 diesel (M57)
5 speed manual with UUC short shifter.
Pre-xDrive NV125 transfer case (chain & gears).
Factory Xenon headlights, Spyder LED tail lights
Updated vortex crankcase breather.
Motorsport dead pedal, factory fire extinguisher, factory first aid kit, factory F&R mud flaps, factory PDC

Bilstein B6 shocks F&R
Redline oil has replaced "lifetime" fluids (F&R diff, manual transmission, transfer case and P/S).
Dimple magnetic drain plugs in all compartments.