I would find out exactly where the speed signal comes from, monitor it and try disconnecting it to see what happens. What does the digital readout show?

What you are calling high beams might be the daytime running lights. If you have Xenon lights then high and low beams are the same light. Your description of what the lights are doing isn't really clear.

By 2000th do you mean the year?

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)