Are you SURE it's a SERVO motor?
Is it belt drive or direct drive? Have you opened up the unit to inspect it?
Belt drive units are usually the more simple DC motors, (not servo). Also, when drive function fails, it's usually the BELT more often than the motor.
Direct Drive units are usually servo motors, which is quite different from belt drive.
Most Tascam Portastudios and Syncasets are belt drive, DC motors, with the exception of the most sophisticated units: the 644, 688 & 238, which have built-in plug-compatible Sync function.
The 238 I'm positive is a Direct Drive Servo motor, as I've just had the opportunity to have one replaced. The 644 & 688 I'm ASSUMING are also Direct Drive Servo motors, which leaves the possibility open that I'm MISTAKEN,... in which case, some more knowledgable member will eventually come along and correct me.
[OT], the Tascam 388 is a BELT drive unit, that uses SERVO function in the tension arms, PLUS a "tach wheel", which in effect achieves the same Sync capability as a Direct Drive servo-type unit. The Servo is used for that spot-on accuracy, that shuttles tape to an accurate set point, and stops on a dime. A non-servo return-to-zero, like on the Tascam 38, will zoom past zero, then reverse,... past zero again, then reverse, and in smaller increments, rock back & forth till it settles on zero. That's NON servo accuracy for'ya.
The Yamaha MT8X, I have no direct knowledge of. You could tell me more. Maybe we've been throwing the term "servo" around too loosely, but that's all I know of the subject. I know what I know, but YMMV. Maybe if you could fill in supporting details, eh?
In most cases, a qualified repair tech might an answer, with maybe YAMAHA FACTORY SERVICE being the best alternative.
Good Luck.