The conditions under which binary black hole (BBH) mergers embedded in active galactic nucleus (AGN) disks produce detectable optical counterparts remain poorly constrained observationally. We report multiepoch optical imaging and spectroscopic follow-up of S240413p, an O4 BBH candidate with 98% classification confidence and one of the smallest sky localizations reported to date ($\sim 61{\mathrm{deg}}^2$), obtained with the T80-South telescope through the S-PLUS Transient Extension Program (STEP). Our observations cover the 99% credible region across epochs that span $\sim 300\mathrm{days}$ postmerger. We prioritize AGN-hosted environments and identify two transient candidates, STEP2024gab/ZTF18acvgziq and STEP2024phe/ZTF19aaflhnr. Southern Astrophysical Research Telescope/Goodman spectroscopy and archival Dark Energy Spectroscopic Instrument spectra yield host supermassive black hole masses of $\log M_{\mathrm{SMBH}}/M_{\odot }=7.15\pm 0.05$ and $8.02\pm 0.04$. We compute predicted flare delay distributions for each host using a thermal radiation-driven outflow emission model and the spectroscopically derived host properties. Migration traps produced by thermal torques occur at $R_{\mathrm{BH}}/R_g\approx {10}^{4.2}$ and ${10}^{3.4}$ for the two hosts, with predicted flare delays spanning tens to several hundred days; our late epoch at $\sim 300\mathrm{days}$ coincides with both the peak of these distributions and the migration trap locations, while early epochs overlap only their tails. An independent five-dimensional detection efficiency analysis using BBH light curves and teglon confirms that $M_{\mathrm{SMBH}}\sim {10}^7–{10}^8{M}_{\odot }$ AGN environments at merger distances of $\sim 0.003–0.012\mathrm{pc}$ are the most favorable for detectable emission, a regime both candidate hosts occupy. We find no confirmed counterpart; a seasonal visibility gap leaves open the possibility that a flare occurred undetected, the merger may not have occurred within the AGN disk itself, or any emission may have been obscured by intrinsic AGN variability. These results demonstrate that long-baseline, AGN-prioritized monitoring is a necessary condition for accessing the highest-probability region of BBH merger parameter space and establish the need for physically informed follow-up strategies in the Rubin/Legacy Survey of Space and Time era.

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• Electromagnetic radiation astronomy
• Optical, UV, & IR astronomy
• Accretion disk & black-hole plasma