An intuition of ambivalence in cognition is particularly strong for complex decisions, for which the merits and demerits of different options are roughly equal but hard to compare. We examined information search in an experimental paradigm which tasked participants with an ambivalent question, while monitoring attentional dynamics concerning the information relevant to each option in different Areas of Interest (AOIs). We developed two dynamical models for describing eye tracking curves, for each response separately. The models incorporated a drift mechanism towards the various options, as in standard drift diffusion theory. In addition, they included a mechanism for intrinsic oscillation, which competed with the drift process and undermined eventual stabilization of the dynamics. The two models varied in the range of drift processes postulated. Higher support was observed for the simpler model, which only included drifts from an uncertainty state to either of two certainty states. In addition, model parameters could be weakly related to the eventual decision, complementing our knowledge of the way eye tracking structure relates to decision (notably the gaze cascade effect).