Polarized time resolved fluorescence measurements are used to characterise the structure of the two-photon tensor in the enhanced green fluorescent protein (EGFP) and predict the "hidden" degree of hexadecapole transition dipole alignment 〈α40〉 created by two-photon absorption (TPA). We employ a new method for the accurate STED measurement of the evolution of 〈α40〉 by analysing the saturation dynamics of the orthogonally polarized components of two-photon excited EGFP fluorescence as a function of the time delay between the 800 nm pump and 570 nm dump pulses. The relaxation of 〈α40〉 by homo-FRET is found to be considerably greater than that for the fluorescence anisotropy which directly measures the quadrupolar transition dipole moment alignment 〈α20〉. Our results indicate that higher order dipole moment correlation measurements promise to be a sensitive probe of resonance energy transfer dynamics.