The T₁(X)( in _g(+) tau _2g) Jahn-Teller system is studied under conditions of equally strong spin-orbit and linear vibronic interactions. Several unitary transformations are introduced which simplify the Hamiltonian, and a representation involving the lowest few total angular momentum eigenstates is set up. This procedure allows for the resonance energies and intensities to be solved for in a manner which improves with increasing coupling strengths. To complement this analysis, an approximate analytical solution is also developed. Comparison with previous matrix diagonalisation results shows good agreement.