Eyetracking technology has had limited application in the dementia field to date, with most studies attempting to discriminate syndrome subgroups on the basis of basic oculomotor functions rather than higher-order cognitive abilities. Eyetracking-based tasks may also offer opportunities to reduce or ameliorate problems associated with standard paper-and-pencil cognitive tests such as the complexity and linguistic demands of verbal test instructions, and the problems of tiredness and attention associated with lengthy tasks that generate few data points at a slow rate. In the present paper we adapted the Brixton spatial anticipation test to a computerized instruction-less version where oculomotor metrics, rather than overt verbal responses, were taken into account as indicators of high level cognitive functions. Twelve bvFTD (in whom spatial anticipation deficits were expected), six SD patients (in whom deficits were predicted to be less frequent) and 38 healthy controls were presented with a 10 × 7 matrix of white circles. During each trial (N = 24) a black dot moved across seven positions on the screen, following 12 different patterns. Participants' eye movements were recorded. Frequentist statistical analysis of standard eye movement metrics were complemented by a Bayesian machine learning (ML) approach in which raw eyetracking time series datasets were examined to explore the ability to discriminate diagnostic group performance not only on the overall performance but also on individual trials. The original pen and paper Brixton test identified a spatial anticipation deficit in 7/12 (58%) of bvFTD and in 2/6 (33%) of SD patients. The eyetracking frequentist approach reported the deficit in 11/12 (92%) of bvFTD and in none (0%) of the SD patients. The machine learning approach had the main advantage of identifying significant differences from controls in 24/24 individual trials for bvFTD patients and in only 12/24 for SD patients. Results indicate that the fine grained rich datasets obtained from eyetracking metrics can inform us about high level cognitive functions in dementia, such as spatial anticipation. The ML approach can help identify conditions where subtle deficits are present and, potentially, contribute to test optimisation and the reduction of testing times. The absence of instructions also favoured a better distinction between different clinical groups of patients and can help provide valuable disease-specific markers.