I had a similar issue with the multi-switch when I first got my car.
Instead of shifting to N, or not shifting, but indicating N such as yours, under similar conditions that you describe, my car would not enagage the M mode when the shifter was set to M. Instead, I got the dreaded 4th gear indicator flashing on the dash, even though the tranny worked perfectly automatically, even though it was set to M.
It turned out that the multi-switch was dirty from road gunk. Ever since cleaned and adjusted, it has worked properly w/o incident.
My guess is that the one you describe is improperly adjusted. There's a fine line in getting it dialed-in or not.
Cheers!
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