This is the second of a series of two papers devoted to the partition
    function realization of Wilson surfaces in strict higher gauge theory. A higher
    2–dimensional counterpart of the topological coadjoint orbit quantum
    mechanical model computing Wilson lines is presented based on the derived
    geometric framework, which has shown its usefulness in 4–dimensional higher
    Chern–Simons theory.

    Its symmetries are described. Its quantization is analyzed in the functional
    integral framework. Strong evidence is provided that the model does indeed
    underlie the partition function realization of Wilson surfaces. The emergence
    of the vanishing fake curvature condition is explained and homotopy invariance
    for a flat higher gauge field is shown. The model’s Hamiltonian formulation is
    further furnished highlighting the model’s close relationship to the derived
    Kirillov-Kostant-Souriau theory developed in the companion paper.

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