BUCS is an emergency back up system, and isn't used normally unless there are issues or seizures in the control system, so wouldn't be used to transfer control...
BUCS = Back Up Control System. So - both pilots/CPGS stations are linked mechanically - in the same way any (most) dual seat helicopter is designed (either side by side or tandem seating arrangement) - so mechanical rods between one station to the other. Move one stick fwd - be it front or aft - the other one should replicate the action.
BUCS is a pseudo emergency 'fly by wire' system - in that the controls are locked into the overall system by cams and springs. The idea being if there is a seizure or failure in the system (bearing failure, pilot shot and leaning against the stick etc) there is an ability to knock the stick out of its mechanical connection by overcoming a certain amount of force - which breaks the stick out of its cams, and from there on in it relies on input into an linear transformer which relays any detected movement electrically to the controlling servos.
OK - just back from 'messing about' swapping between stable and beta. First question - have you purchased and installed A10C2? The reasons for the question is that the mission appears to be set to 'fly' a C2 model.
Went into 2.7 - training - mission 5 Navigation - opened no problems - started sat in cockpit with brief ongoing. Selected external view, no problems, F1 - back in the seat. Back to F2 - whoa...no PavePenny Pod!? Closed mission - started it up again - same. Watched the mission launch as it loaded - had the C2 graphic (side view of a A10) and not the C (front view with flames) and C2 was displayed above the load bar.
Went into 2.5 - same as above. Opened mission 4 and 6 - all good with an A10C.
Easy fix though. Located the training mission folder for the A10C in the main DCS folder, copied and pasted it into my Saved Games mission folder (otherwise you cannot see it in the mission editor) - opened it in Mission Editor - sure enough - aircraft type set to A10C2. Changed it back to A10C, saved, copied and then pasted it back into original training mission A10C folder. Re-opened 2.7, training, Navigation - aircraft now A10C.
Leg2ion's post in How does BUCS Select work ? was marked as the answer