Fixed that (thank you autocorrect) deflection
When the arm is up it should self-center and resist being moved away from that position.
If the self centering function isn't working, it can be anywhere in it's arc of movement it has, even when up or parked.
And, if it isn't centered when up, the servo will try to correct for this as it's lowering (I think

) and the carriage will move in the direction of it's deflection.
Sounds like the servo functions normally.
When it finally gets in the groove of a record, I assume it tracks it and stays tangential to it, i.e.: straight out from the carriage, 90* to the tracks it moves on, following the inward travel of the groove while staying tangential to it.
If it's parking straight out/arm resists being moved from it's center position, then probably that linkage isn't a problem.
If you cue it into the gap before the platter and hold it, it goes to tangent position and stays unless you move the head shell left or right, correct?
If yes, then what happens if you let go of it? does the arm want to move inwards and the servo "chases" it (as it should)
If so, what is the causing the force that makes the arm move/twist on its gimbals? Is the turntable grossly out of level? Is the force so small that you can counter it by lifting the other side of the turntable to counter it? Can you look with a small light into the fulcrum area for some small debris (like a down feather) that got in there and is causing a force, almost like anti-skate force on a conventional arm?
Time for bed!