The question is
The stab has 3 position transducers that feed to their onside FCU. Why does the loss of 1 transducer cause a T/O config warning?
Anybody with access to their training notes
On the B744
The Left stab position sensor provides position indication to the left/Cpt's stab trim position.
The right stab position sensor to the right/Fo's stab trim indicator.
Hence you can get a position disagree visible between the two indications
The centre sensor provides data to the takeoff config warning system.
So a loss of centre data or a error from the centre stab positon indicator will cause a takeoff config warning anytime during the roll.
I believe most large commercial jets require the three independant sensors for certification requirements whether boeing or airbus, but someone more knowledgeable may be able to correct me if not the case.
MC