The results of conventional deep-level transient spectroscopy (DLTS) and high-resolution Laplace DLTS measurements of the FeGa(0/−) acceptor level in dilute AlxGa1−xN layers (x ≤ 0.05) grown by MOVPE technique (metal–organic vapor phase epitaxy) on native ammono-GaN substrates are analyzed and discussed. It is shown that the electron emission signal related to the FeGa acceptor level in AlxGa1−xN splits into individual components due to aluminum fluctuations in the second-nearest neighbor (2NN) shell around the FeGa impurity atoms. The calculations of the probability of finding a given number of aluminum atoms in the 2NN shell of the FeGa defect agree well with the experimental concentrations determined from Laplace DLTS peak intensities. This finding shows that in dilute AlxGa1−xN layers grown by MOVPE, aluminum and iron atoms are randomly distributed in the material. Finally, we demonstrate that the energy level of the FeGa acceptor with no Al atoms in the 2NN shell in the AlxGa1−xN samples shifts linearly with the aluminum content and the shifts are 28 and 55 meV relative to that in GaN for the samples with x = 0.025 and 0.05, respectively.