If the crank sensor is of unknown origin...that would be suspect just because aftermarket electronic things never seem to do well in our cars.
Those lights are pretty common, I think, and they indicate more than you think just because you can also 'manually' control them. If you search for them in a 'thread title search' I'm sure you'll find some useful threads.
I remember a few threads with cutting out while driving. It can just be loose cable on battery too, corrosion somewhere on one of the major grounds?
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Mangofy your E46!