The timeline of cosmic reionization remains uncertain despite sustained efforts to study how the ionizing output of early galaxies shaped the intergalactic medium (IGM). Using the seminumerical code LIMFAST, we investigate the prospects for timing the reionization process by cross-correlating the 21 cm signal with the cosmic near-infrared background (NIRB) contributed by galaxies at z > 5. Tracing opposite phases of the IGM on large scales during reionization, the two signals together serve as a powerful probe for the reionization history. However, because long-wavelength, line-of-sight Fourier modes—the only modes probed by NIRB fluctuations—are contaminated by 21 cm foregrounds and thus inevitably lost to foreground cleaning or avoidance, a direct cross correlation of the two signals vanishes. We show that this problem can be circumvented by squaring the foreground-filtered 21 cm signal and cross-correlating the squared field with the NIRB. This statistic is related to the 21 cm–21 cm–NIRB cross bispectrum and encodes valuable information regarding the reionization timeline. Particularly, the 21 cm2 and NIRB signals are positively correlated during the early phases of reionization and negatively correlated at later stages. We demonstrate that this behavior is generic across several different reionization models and compare our simulated results with perturbative calculations. We show that this cross correlation can be detected at high significance by forthcoming 21 cm and NIRB surveys such as the Square Kilometre Array and SPHEREx. Our methodology is more broadly applicable to cross correlations between line intensity mapping data and 2D tracers of the large-scale structure, including photometric galaxy surveys and cosmic microwave background lensing mass maps, among others.