OK, solved it! Inside edit mode – I made sure that the Owner bone (The bone who has the Locked Track constraint) – has its axes aligned with the world axes (Meaning the bone’s local Y is the same as the world’s Y, the local Z is the same as the world’s Z etc.) Then once I applied the Locked track it behaved as expected (Rotating around its Z axis, having the local Y axis pointing towards the Target bone)
Hope my question (and solution) are clearer now.
