We study the problem of identifying individuals based on their characteristic gaze patterns during reading of arbitrary text. The motivation for this problem is an unobtrusive biometric setting in which a user is observed during access to a document, but no specific challenge protocol requiring the user's time and attention is carried out. Existing models of individual differences in gaze control during reading are either based on simple aggregate features of eye movements, or rely on parametric density models to describe, for instance, saccade amplitudes or word fixation durations. We develop flexible semiparametric models of eye movements during reading in which densities are inferred under a Gaussian process prior centered at a parametric distribution family that is expected to approximate the true distribution well. An empirical study on reading data from 251 individuals shows significant improvements over the state of the art.