How long has it been out? You may have tripped the short circuit counter on that turn signal which needs to be reset via Tool32. If that happened, the car shuts down that circuit entirely which could explain why it's not turning on even with the new tail light assembly.
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'16 M3 | '23 718 Spyder
Past: E92 M3, F87 M2, E39 M5, etc
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