Why do the stabiliser trim wheels not move exactly in sync?
The rear wing (horizontal stabilizer) of a 737 is effectively one piece. There is no separate left and right trim control. Both sides during assembly are attached as one.

This is just a visual illusion because the white marks are not aligned. If you manually move one wheel, both wheels will move.

It's worth noting that the white marks do not represent the position. For the full stabilizer travel, the wheels would make many, many revolutions.

The stab trim position indicators would show the position, not the wheels:


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