Some relevant aspects of the instability of Geodesic Acoustic Modes (GAMs) driven by Neutral Beam (NB) injection are studied, in particular its dependence on the injection direction, that is, co- or counter-injection, and on the pitch angle distribution of the beam particles in velocity space. In this paper, we further investigate these and other related issues considering the excitation of GAMs by energetic ions created during NB injection and modeled by a bump-on-tail distribution function with a sharp Gaussian dependence over the pitch angle at the injection angle. The bump is considered to have an energetic ion tail with temperature of the order of the third part of the critical energy that appears due to the slowing down effect on electrons. It is found that the maximum frequency of the GAM instability stays below the particle circulation frequency at the critical energy, and it is substantially reduced to be closer to parallel injection conditions. The instability may be preferentially driven for counter NB injection due to the interaction of plasma rotation and/or diamagnetic drift with electron current velocity.