Active feedback stabilization of the vertical instability is studied for highly elongated tokamak plasmas (2 less-than-or-equal-to kappa less-than-or-equal-to 3) and evaluated in particular for the TCV configuration. It is shown that the feedback can strongly affect the form of the eigenfunction for these highly elongated equilibria, and this can have detrimental effects on the ability of the feedback system to detect properly and stabilize the plasma. A calculation of the vertical displacement that uses poloidal flux measurements, poloidal magnetic field measurements, and corrections for the vessel eddy currents and active feedback currents was found to be effective even in the cases with the worst deformations of the eigenfunction. These deformations are also examined to determine how they affect equilibria with various degrees of shaping, and it is seen that the magnitude of the deformation of the eigenfunction is a strong function of the plasma elongation.