Sometimes the no turn sig situ can be 'fixed'/stalled with cleaning the turn signal bulb contacts; a knuckle busting job, in my experience.
Or, a new relay(s) wiring harness: pretty inexpensive, not hard to replace, but a good BMW Indie will have seen/done dozens of that repair on various models of
BMWs, and can fix it 15 mins. If it isn't the bulb(s), bulb contacts, or relay(s), I have no clue...
'01 X5 3.0 Sport, 5 Spd Manual, etc.
'02 VetteVert 6 Spd, Z51 susp.
'10 Hyundai Tucson for the CEO, & 3 Assorted M'Cycles.
BMW CCA mem. Tarheel Chapter