J0404+1112: A 3-Hour Eclipsing White Dwarf-Brown Dwarf Probing Multiple Atmospheric Regimes

White dwarf-brown dwarf (WD+BD) binaries are rare laboratories for probing both substellar survival through post-main-sequence evolution and the physics of strongly irradiated atmospheres. We present time-resolved eclipse photometry and radial-velocity confirmation of J0404+1112, a compact ($P = 2.93$ hr), totally eclipsing WD+BD system initially reported in a Research Note of the AAS. New high-cadence observations resolve a total eclipse of the WD and, combined with spectroscopy, broadband photometry, and the Gaia parallax, yield a revised system architecture. We find a hot DA WD with $T_{\rm eff} \simeq 28{,}000$ K, $\log g \simeq 8.0$, $M_{\rm WD} \simeq 0.6 \rm{M}_\odot$, and $R_{\rm WD} \simeq 0.015 \rm{R}_\odot$, orbited by a $\sim40 \rm{M}_{\rm Jup}$ BD with radius $\sim0.9 \rm{R}_{\rm Jup}$. These parameters supersede earlier SED-based estimates in which the WD temperature, radius, distance, and extinction were strongly covariant. We break this degeneracy with normalized Balmer-line profile fitting and high-cadence eclipse photometry that constraints the WD's radius geometrically. The total eclipses enable isolation of the BD flux and constrain its nightside emission. With its short orbital period and strong irradiation, J0404+1112 provides a uniquely compact, high-sensitivity JWST benchmark for probing atmospheric heat redistribution and photochemistry in the temperature regime of the hottest ultra-hot Jupiters, spanning dayside and nightside brightness temperatures of $\sim3{,}600$ K and $\sim1{,}800$ K within a single $\sim$3 hr orbit.