We report on the Mg-doped, indium-rich Ga (x) In1-x N (x < 30). In the undoped material, the intrinsic electron density is very high and as a result there is no detectable photoconductivity (PC) signal within the range of temperatures of 30 < T < 300 K. In the Mg-doped material however, where the conductivity is reduced, there is a strong PC spectrum with two prominent low-energy peaks at 0.65 and 1.0 eV and one broad high-energy peak at around 1.35 eV. The temperature dependence of the spectral photoconductivity under constant illumination intensity, at T > 150 K, is determined by the longitudinal-optical phonon scattering together with the thermal regeneration of non-equilibrium minority carriers from traps with an average depth of 103 +/- 15 meV. This value is close to the Mg binding energy in GaInN. The complementary measurements of transient photoluminescence at liquid He temperatures give the e-A(0) binding energy of approximately 100 meV. Furthermore, Hall measurements in the Mg-doped material also indicate an activated behaviour with an acceptor binding energy of 108 +/- 20 meV.