If you want to drive a universal joint in two degrees of freedom, the typical way to do it is to extend the "+" in the universal joint, and couple them to the horn of a servo. The servo rotating will then push one end and pull the other end of the plus, and it will move. You can mount one servo on each link connecting to the plus.
Note that using a ball joint for a 2-dof arm is less robust than using a universal joint, because you will get torque on the joint which will have to be absorbed only by the control assembly, in directions it is not designed to be strong.