The A(2)Pi(u) -X-2 Pi(g) and 1(4)Sigma(-)(u)-X-2 Pi(g) electronic transition spectra of Br2+ have been studied in the 500-720 nm wavelength range in a cold ion beam using a cryogenic cylindrical ion trap velocity map imaging spectrometer. The cryogenic ion trap produces a rotationally and vibrationally cold mass selected ion beam of Br-2(+), which simplifies the experimental spectra from vibrational hot bands and bands of mixed isotopic species. Vibrationally resolved photofragment excitation spectra are recorded for individual isotopologues of Br2+ (Br-79(2)+,(BrBr+)-Br-79-Br-81, Br-81(2+)) by [1+1] two-photon dissociation spectroscopy. Velocity map imaging of the photofragmented Br+ ions provides complementary information in the determination of spin-orbit states involved in corresponding electronic transitions. An experimental identification of the 1(4)Sigma(-)(u) state has becomes possible based on the present experimental results and previously reported theoretical calculations. Vibrational analyses of the photofragment excitation spectra have yielded spectroscopic parameters, including state origins, harmonic frequencies, and anharmonic constants, for both A(2)Pi(u) and 1(4)Sigma(-)(u) states. The observed A(2)Pi(u) state spin-orbit splitting and the "spin-forbidden" 1(4)Sigma(-)(u)-X-2 Pi(g) transition band intensities indicate considerable spin-orbit couplings between the 1(4)Sigma(-)(u) and A(2)Pi(u) states. In addition, two groups of weak vibrational bands are also observed in the experimental spectra of (BrBr+)-Br-79-Br-81, which may be due to symmetry-forbidden transitions from the X-2 Pi(g) ground state to low-lying gerade states.