A 'variational' process and a 'recursion' scheme applied to a multimode dynamic Jahn-Teller Hamiltonian have recently been shown by Fletcher, O'Brien and Evangelou (see J. Phys. A: Math. Gen., vol.13, p.2035, 1980) to reduce into the single-frequency cluster model, corresponding to weak and strong electron-phonon coupling limits where narrow bands ( approximately 102 cm-1) with a sharp-zero-phonon line and broad ( approximately 103 cm-1) absorption bands are observed respectively. A functional-integral formalism is presented for the optical response function of a general pseudo-Jahn-Teller model system which includes the coupling of the nearly degenerate 2s and 2p excited states to lattice phonons, appropriate to describe in some cases the F centre in alkali halides and the bound polaron problem. Band shapes derived in the independent ordering approximation (10A) do not give the details of the broad bands as shown in the comparison with the numerical spectra within the cluster model, at T=0K. It is further shown that the IOA does take into account the phonon dispersion of the host lattice at weak and strong coupling, in a manner equivalent to the two cluster model descriptions.