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I assume you have the tamper dot. This video shows a solution: https://m.youtube.com/watch?v=XRbUdOpYVUo It is easier than NCS expert though the cables are different.

Carsoft is generic isn't it? I would say it may well not be good enough. Inpa or PA soft would be better. It may well be the LCM or otherwise maybe check the connections on the bulb holders including the earths. There are also posts on other forums suggesting that old bulbs that are on the way out can cause such intermittent symptoms. Some new bulbs might be worth a try.

I haven't seen one for years. Maybe since the 80s. They were not popular and only made for a couple of years in the late 60s. Only a few thousand made. Intended to replace the big healey, the 3 litre 145hp engine was heavy and imapcted on the handling. MGBs didn't handle great anyway. The latter had leaf springs amd lever arm dampers like a marina or minor I recall.

MGC Roadster with the 6 cylinder 3 litre engine.

I had a nice one of these in oxford green before my E39. This one looks reasonable. https://www.carandclassic.com/make-an-offer/1994-bmw-525i-se-touring-e34-nAbE74

Pretty sure these are two separate systems each with its own relay. So if headlight washer and wimdscreen washer pumps are not working that would not be a common failure point. https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://www.bimmerfest.com/attachments/bmw-e39_general_wiring_diagrams_color-pdf.441296/&ved=2ahUKEwif87ntirWHAxVPXEEAHW6pDLI4FBAWegQIBxAB&usg=AOvVaw15jJiLJdSrm8H5XcPyO8zU

You might try clear head upholstery twist pins. Depends on how much space there is behind.

My understanding is that the needle is electronic not just a vacuum guage but behaves a bit like one. Not necessarily accurate but intended to help with an ecomical driving style. It may be possible to test the cluster: https://m.youtube.com/watch?v=0kyMmE3XW5s It may also be possible to reset the cluster. Doing this without a laptop would be with the secret menus and you would need to google that. Ideally one would want to be testing this with diagnostics plugged in, such as INPA. One other thing you might try, as it is free and only takes 5 minutes (though it probably won't work) is to disconnect the battery and hold the positive and negative battery cable connectors together for a minute or so. Ultimately it might end up that a cluster repair is needed, which could be about £200. Maybe not worth it just for that needle.

https://www.bimmerforums.com/forum/showthread.php?2129956-Steering-rack-seal-replacement-with-rack-in-car

I would say no chance. Maybe wrong: https://tfl.gov.uk/modes/driving/check-your-vehicle/Results Easy enough to find a few number plates online. Try: P445 VGT R511 DEP T279 SPK All come up £12.50 per day

This is who I have been using for batteries, based on previous advice on this forum. https://www.tayna.co.uk/ Yuasa or Bosch. In the case of my two BMWs, the former.

I suspect this relates to the later DSC module as per the post from Sir Anthony. I had the same issue on my 2002 530i. Thought it was a sensor but it was the module. They are hard to repair and mine had already been repaired once. I fitted a new old stock module. All this probably not relevant here as it is an earlier module. Looks different from mine in that picture.

One on ebay now. Not cheap. https://www.ebay.co.uk/itm/186443756854?itmmeta=01HYFGKZ5440D60SG5YV1ZSHB6&hash=item2b68e9f536:g:Y4sAAOSwfHFmHBi9&itmprp=enc%3AAQAJAAAA4JasyUeVElJZJbHtebqgBaPFLxI1SOnDBfl0Pbtp7kHtRuprP%2BxDviOK84Jm4GH%2B8sVd6sToVtKCDfJzHd0ySW8bUdXU0UTNfSA0tqSmDuWqr6mGCj%2BBDsRItLrnABWOkOAHVLfApQ5i48naakcX05Rf3B1fqmCOyXCrTV4yzfmnRkKcM4NV0GSRRip3n3rBULUZknGnYoblyJ4eBeWDwH0Jkij%2FOqtB5r804snApgylr7a5z3FbIA1OKbRGTkQ1kFJD601kQas1r5hNBQXcrnoRqWDE5tSMtf8JlQBgKbAK|tkp%3ABk9SR9Dyz_DzYw When I had an E34 Touring I could not find a genuine set at a reasonable price so I made my own. I used a Thule Foot Pack for a Fiat Ulysse (1990s). Forgot the number. They have embedded channels. To attach it I used M6 cage nuts in the channels. It worked very well for years with a 6ft roof box.

I was also looking at JT automatics in Erith. Good reviews for them also and what looks like a E46 parked outside on the website. https://www.automatic-gearbox.co.uk/