Besides living in the infirmary most of the time, not much. Beign a member of the GB is not what it used to be years ago. Part of the problem is finding enough 'qualified' anointed men to run the show. Hence they have had to resort to those of the 'other sheep' to carry most of the load. Because of the shifting of this the balance of power has had to be distributed among the many different committees. That is why you hear of the power struggle going on within the WT and it's various committees and departments, esp. Service, Writing, and Legal.
The only figure head that somewhat emerges from the GB class with any wielding authority is T. Jaracz. But even he is having to deal with his own demons, and is not liked by some members of the GB and many of the Bethel family.