Can you confirm that the charge lamp lights up full brightness when the ignition is first turned on - before the engine is running?
The TIS states: -
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Charge indicator lamp
Terminal D+ is replaced by an isolated electronic terminal 61E in alternators with a multifunction controller. The task of this terminal is, on the one hand, to activate the battery charge indicator lamp and, on the other hand, to indicate to the various loads that the alternator is in charge mode.
The battery charge indicator lamp itself is supplied via terminal 15 from the instrument cluster. It comes on when the voltage at terminal 61E is below 1.5 V. The battery charge indicator lamp goes out when the voltage at terminal 61E is above 8 V.
Alternators with a multifunction controller can be recognized by the plug connection of terminal 61E. As a result, the 6 mm threaded stud has been dispensed with.
The indicator lamp lights up when:
Ignition on with engine stationary, alternator does not charge, failure of belt drive, interruption in excitation, controller overvoltage, break in charging cable
The second cable in the plug connection at the alternator is terminal 15 that serves as a reference signal for determining whether the alternator is charging.
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The actual circuit layout varies from the earlier pre-facelift (M57) cars to the later LCI (M57TU) cars: -
M57
M57TU
Measuring the voltage on terminal 61-1 would perhaps give a clue as to why the lamp is lit