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We adapt a method, originally developed for searches for quasi-monochromatic, quasi-infinite gravitational-wave signals, to directly detect new light gauge bosons with laser interferometers, which could be candidates for dark matter. To search for these particles, we optimally choose the analysis coherence time as a function of boson mass, such that all of the signal power will be confined to one frequency bin. We focus on the dark photon, a gauge boson that could couple to baryon or baryon-lepton number, and explain that its interactions with gravitational-wave interferometers result in a narrow-band, stochastic signal. We provide an end-to-end analysis scheme, estimate its computational cost, and investigate follow-up techniques to confirm or rule out dark matter candidates. Furthermore, we derive a theoretical estimate of the sensitivity, and show that it is consistent with both the empirical sensitivity determined through simulations, and results from a cross-correlation search. Finally, we place Feldman-Cousins upper limits using data from LIGO Livingston's second observing run, which give a new and strong constraint on the coupling of gauge bosons to the interferometer.