Does the 119 share any components in the TR drive train with the 429? particularly TR servos.
I only ask because a friend had uncontrolled yaw on the ground in one and it took a long time for the fault to be acknowledged.
No the physical components aren't the same, but then it wasn't the tail rotor servos at fault on the Bell 429 (I make the assumption that by servo you mean the hydraulic servo). I don't think you're on the wrong track though (see later). For context the AW119 is essentially a single engine skidded variant of the A109E.
In the Bell 429 incidents it was the trim actuator building up a huge out of trim force through a "normal" AFCS mode. But that doesn't seem to it the situation here. The yaw rate happens as the aircraft is started so I assume the AFCS is not active at this point and therefore I think it's not the trim actuator. It's a left (power pedal) yaw so this indicates the tail rotor was functioning at very high power so a drive disconnect can be discounted. The pilot would be unlikely to have his feet away from the pedal and should naturally stomp down right pedal to stop a left yaw so the control run may be at fault.
However, back to your original point. I do think a hydraulic servo jam or runaway (there is a single servo in the yaw channel on AW119) could give the symptoms, which was what they originally thought had happened on the 429. I hope the investigation works it out