Given the very close proximity of their habitable zones, brown dwarfs (BDs) represent high-value targets in the search for nearby transiting habitable planets that may be suitable for follow-up occultation spectroscopy. In this paper, we develop search strategies to find habitable planets transiting BDs depending on their maximum habitable orbital period (P HZ out). Habitable planets with P HZ out shorter than the useful duration of a night (e.g., 8-10 hr) can be screened with 100% completeness from a single location and in a single night (near-IR). More luminous BDs require continuous monitoring for longer duration, e.g., from space or from a longitude-distributed network (one test scheduling achieved three telescopes, 13.5 contiguous hours). Using a simulated survey of the 21 closest known BDs (within 7 pc) we find that the probability of detecting at least one transiting habitable planet is between 4.5^{+5.6}_{-1.4}% and 56^{+31}_{-13}%, depending on our assumptions. We calculate that BDs within 5-10 pc are characterizable for potential biosignatures with a 6.5 m space telescope using ~1% of a five-year mission's lifetime spread over a contiguous segment only one-fifth to one-tenth of this duration.