Manipulation

The stick is easy to manipulate by moving the "controler" empty object (see video) - all involved objects have appropriate constraints (eg. limit rotation, locked track, transformation) and will follow the "controler" automatically.
The "controler" can be also rotated along its local Z axis to twist the stick (rudder control).
Both throttles can be adjusted separately by rotating "throttle_L01" and "throttle_L02" along their local Y axes (rotation range is limited by constraints, locks are set for X and Z axes).
The "throttle_L02" object (to bind both throttles in real product) has 'limit locaton' constraint and location locks for X and Z axes to keep it easy to adjust.

Optional parts

The wrist rest on the lower part of the stick is optional (removable) in real product. To get rid of the wrist rest, "stick_wrist01", "stick_wrist02", "screw_wrist01" and "screw_wrist02" should be hidden, moved to hidden layer or deleted.