This paper explores Fano resonances due to non-adiabatic coupling of vibrational modes and the electron continuum in dipole-bound anions. We adopt a simple one-electron model consisting of a point dipole and an auxiliary potential to represent the electron interaction with the neutral core. Nuclear motion is added by assuming that harmonic vibrations modulate the dipole moment. When the model is parameterized to simulate key features of the water tetramer anion, the resultant photodetachment lineshape closely resembles that observed experimentally and analyzed as a Fano resonance with a parameter q close to -1. Other parameterizations are explored for the model and it is found that large changes in the auxiliary potential are required to change the sign of q. This is consistent with the experimental finding that q is negative for all water cluster sizes studied.