If the fault codes point towards the F125 switch, I would check the condition of its connector first.
One of my previous '8s had similar issues. On inspection, the connector was in a similar condition to the one in this article:
click -- Cleaning the connector fixed the problem.
The connector seems to be fairly prone to corrosion, but in my case it was made all the more vulnerable because the
bottom engine tray/cover (aka the 'noise insulation' cover) was missing. Often they're removed for servicing and never refitted. My present S8's was also missing when I bought it (and it cost me £70 for a new one!).
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Mark
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2002 FE S8 Ebony Black Pearl
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Cars Owned:
The Tesla Era: 2020 Model S Performance Ludicrous+ (present)
(Black, with all black premium interior and carbon fibre décor, 21" sonic carbon twin turbine wheels and FSD capability)
The Audi Era: '97 A8 4.2 (Ming Blue) --> '96 A8 4.2 QS (Dark Green) --> '02 FE S8 (present)
The Citroen Era: '84 BX 1.6 RS --> '89 BX 1.9 DTR Turbo --> '94 XM 2.0L Turbo --> '96 XM 2.0L Turbo Exclusive --> '00 Xantia Activa 2.0L Turbo
The Banger Era: '76 1.2L Lada VAZ-2101 (Ruski Fiat 124) --> '80 1.7L Morris Ital HL, finished in Ermine White and Rust