Well, I’m really baffled and glad… This issue has been resolved.
I haven’t been able to pinpoint the cause, but I’ve noticed something suspicious.
When using LiveLink in MotionBuilder, I habitually accidentally linked LiveLink twice.
As a result, there are two LiveLinks in the I/O device list, just like the reference image.
So I didn’t hook up any additional LinkLinks, and Timecode works great!