Objective: Delirium, an acute confusional state, affects 20-80% of patients in Intensive Care Units (ICUs), one in three medically hospitalized patients, and up to 50% of all patients who have had surgery. Its development is associated with short- and long-term morbidity, and increased risk of death. Yet, we lack any rapid, objective, and automated method to diagnose delirium. Here, we detail the prospective deployment of a novel dual-camera contextual eye-tracking platform. We then use the data from this platform to contemporaneously classify delirium. Results: We recruited 42 patients, resulting in 210 (114 with delirium, 96 without) recordings of hospitalized patients in ICU across two centers, as part of a prospective multi-center feasibility pilot study. All recordings made with our platform were usable for analysis. We divided the collected data into training and validation cohorts based on the data originating center. We trained two Temporal Convolutional Network (TCN) models that can classify delirium using a pre-existing manual scoring system (Confusion Assessment Method in ICU (CAM-ICU)) as the training target. The first model uses eye movements only which achieves an Area Under the Receiver Operator Curve (AUROC) of 0.67 and a mean Average Precision (mAP) of 0.68. The second model uses the point of regard, the part of the scene the patient is looking at, and increases the AUROC to 0.76 and the mAP to 0.81. These models are the first to classify delirium using continuous non-invasive eye-tracking but will require further clinical prospective validation prior to use as a decision-support tool. Clinical impact: Eye-tracking is a biological signal that can be used to identify delirium in patients in ICU. The platform, alongside the trained neural networks, can automatically, objectively, and continuously classify delirium aiding in the early detection of the deteriorating patient. Future work is aimed at prospective evaluation and clinical translation.