Hi, my name is Paul & I will try to assist you.
The noise is almost certainly one of the heater flap motors behind the dash - the drive between the motor & the heater housing often break causing this clicking noise.
the motors do a sweep to each stop when you first switch on - when the drive breaks the flap forced the drive past the stop which causes the clicking noise - this continues for a few minutes when the motor will stop trying to reach the end stop position.
there are around 8-10 different motors on the heater housing & the fault can be any one of them - some of the motors can be removed by taking off dash trims - others need the complete dash & heater housing removed to acces them (over 10 hours work!)
to identify which drive is at fault the car should be checked on Mercedes STAR diagnostic tool - this will have stored a fault with the bad motor & drive in the AC control unit
Best regards, Paul