Clickstreams on individual websites have been studied for decades to gain insights into user interests and to improve website experiences. This paper proposes and examines a novel sequence modeling approach for web clickstreams, that also considers multi-tab branching and backtracking actions across websites to capture the full action sequence of a user while browsing. All of this is done using machine learning on the client side to obtain a more comprehensive view and at the same time preserve privacy. We evaluate our formalism with a model trained on data collected in a user study with three different browsing tasks based on different human information seeking strategies from psychological literature. Our results show that the model can successfully distinguish between browsing behaviors and correctly predict future actions. A subsequent qualitative analysis identified five common web browsing patterns from our collected behavior data, which help to interpret the model. More generally, this illustrates the power of overparameterization in ML and offers a new way of modeling, reasoning with, and prediction of observable sequential human interaction behaviors.