What causes the ball to not be centered in a slip/skid?
It is the same thing that makes you slide sideways in your seat going around a corner in your car.
Or the same thing that would cause you to slide sideways the other way if you were driving straight ahead on a side hill.
Don't overthink it... the ball simply responds to the same forces you feel.
ADDENDUM:
“I agree the comparisons are spot on if you are only considering a coordinated turn, but I'm asking about a steady level turn in which the aircraft is slipping/skidding; which I don't think the comparison can easily be extended to?”
I actually think it is the other way around.  Consider the following:
•   CAR - Unless it is travelling on a banked racetrack, at precisely the speed the banked turn was designed for, a car will never be able to make a “coordinated turn”.  There will generally always be a centrifugal sideforce.
•   PLANE - Once adverse yaw at the turn initiation has been countered, and when established in a constant angle of bank turn, most (positively stable) aircraft will default to a coordinated turn.
In case it helps further, let’s take the aircraft “uncoordinated turn” to a couple logical extremes:

Wings Level, unbanked turn, using rudder only.  Think about this as it compares to turning a car on level ground.  This is an exaggerated skidding turn, with all the centrifugal force pulling you (and the ball!) horizontally, or sideways.

Straight ahead, level flight in a side slip.  The aircraft nose is tracking straight ahead and not turning, while the wings are banked.  This is an exaggerated slipping turn, (minus actually turning...) and is just like the example of driving your car on a side hill.  In this case, gravity is pulling you (and the ball!) vertically straight down, which from the aircraft's frame of reference, is a bit sideways.


The ball is a &quot;dumb&quot; instrument.  Nothing more than ball in a tube reacting to centrifugal force and gravity.  You could accomplish the same thing by holding a full glass of water between your knees:  If the inside knee gets wet it is a slipping turn, if the outside knee gets wet it is a skidding turn.
If these explanations are inadequate the only thing left to suggest is that you find a local flight school that offers orientation flights and ask the pilot to demonstrate for you.
If that suggestion isn't practical or affordable, try this simple experiment:  Get a round mixing bowl and a marble.  The round bowl simulates the curve of the glass tube.  Put the marble in the bowl and hold it at arms length and begin turning in place.  (if you think you might get dizzy and fall against the furniture, wear a helmet!)  Your goal is to adjust the angle of the bowl to keep the marble in the center.  Note that if you tip the bowl too much either way the marble will start to roll up the sides.
It isn't a perfect comparison because it doesn't simulate yaw, but can you appreciate the correlation?  Please let me know if any further explanation is needed...