This study evaluates a smartphone-based, deep-learning eye-tracking algorithm by comparing its performance against a commercial infrared-based eye tracker, the Tobii Pro Nano. The aim is to investigate the feasibility of appearance-based gaze estimation under realistic mobile usage conditions. Key sensitivity factors, including age, gender, vision correction, lighting conditions, device type, and head position, were systematically analysed. The appearance-based algorithm integrates a lightweight convolutional neural network (MobileNet-V3) with a recurrent structure (Long Short-Term Memory) to predict gaze coordinates from grayscale facial images. Gaze data were collected from 51 participants using dynamic visual stimuli, and accuracy was measured using Euclidean distance. The deep learning model produced a mean error of 17.76 mm, compared to 16.53 mm for the Tobii Pro Nano. While overall accuracy differences were small, the deep learning-based method was more sensitive to factors such as lighting, vision correction, and age, with higher failure rates observed under low-light conditions among participants using glasses and in older age groups. Device-specific and positional factors also influenced tracking performance. These results highlight the potential of appearance-based approaches for mobile eye tracking and offer a reference framework for evaluating gaze estimation systems across varied usage conditions.