So thats why I couldn't find my earlier post... it wasn't a post it was a PM to DavidS. The following might help, if not try PM'ing DavidS since he was actually working on an E39 cluster at the time.
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This is going back almost 10 years for my memory

but I'll try to remeber. I have never had a cluster out of the E39 and I had to *completely* de-assemble the ones I worked on, including hard wirring new cicuits we designed onto the existing board and replacing some of the mouldings (the black one) with custom ones we designed. For that reason I may not be the best person to explain how to dismantel in a manner that leaves the bits able to be reassembled.
There where 3 main moldings. From the front:
1. Black at the front that included the perspex front. This was the first one to remove. I think from the rear (mounted through the blue + white moulding) by screws.
2. White was next and servered as the front cover to the circuit board and the moulding into which the gages and the rectangle LCD plugged. All the gauges and LCD were designed to be plugged into the white molding (and the circuit board inside) without any fasteners at all.
3. If I've guessed correct (and this was 10 years ago remember, perhaps things hjave moved on). You have hinged the blue back molding out. This does not help much. You will see the pins from the gauges coming through. You will also see that the cicuit board is heat/melt welded onto the blue molding riverts.
I think (and this is only a suggestion - I don't know) that you need to get the black molding off the white molding as the LCD is mounted in between.
Please remeber that dust becomes a pain in the arse the moment you acheive this.
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One last attempt to help in a poor weird diagram:
1. Black Housing, inc perspex front.
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mounted from screws from back
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2. LCD & gauges
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mounted down into white housing
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3. White housing
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plugged / hinged into blue housing
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4. circuit board
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mounted onto blue moulding
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5. Blue housing
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