Eye tracking (ET) technology is increasingly utilized to quantify visual behavior in the study of the development of domain-specific expertise. However, the identification and measurement of distinct gaze patterns using traditional ET metrics has been challenging, and the insights gained shown to be inconclusive about the nature of expert gaze behavior. In this article, we introduce an algorithmic approach for the extraction of object-related gaze sequences and determine task-related expertise by investigating the development of gaze sequence patterns during a multi-trial study of a simplified airplane assembly task. We demonstrate the algorithm in a study where novice (n = 28) and expert (n = 2) eye movements were recorded in successive trials (n = 8), allowing us to verify whether similar patterns develop with increasing expertise. In the proposed approach, AOI sequences were transformed to string representation and processed using the k-mer method, a well-known method from the field of computational biology. Our results for expertise development suggest that basic tendencies are visible in traditional ET metrics, such as the fixation duration, but are much more evident for k-mers of k > 2. With increased on-task experience, the appearance of expert k-mer patterns in novice gaze sequences was shown to increase significantly (p < 0.001). The results illustrate that the multi-trial k-mer approach is suitable for revealing specific cognitive processes and can quantify learning progress using gaze patterns that include both spatial and temporal information, which could provide a valuable tool for novice training and expert assessment.