  The extragalactic background light (EBL) consists of integrated light from
all sources of emission throughout the history of the universe. At
near-infrared wavelengths, the EBL is dominated by stellar emission across
cosmic time; however, the spectral and redshift information of the emitting
sources is entangled and cannot be directly measured by absolute photometry or
fluctuation measurements. Cross-correlating near-infrared maps with tracers of
known redshift enables EBL redshift tomography, as EBL emission will only
correlate with external tracers from the same redshift. Here, we forecast the
sensitivity of probing the EBL spectral energy distribution as a function of
redshift by cross-correlating the upcoming near-infrared spectro-imaging
survey, SPHEREx, with several current and future galaxy redshift surveys. Using
a model galaxy luminosity function, we estimate the cross power spectrum
clustering amplitude on large scales, and forecast that the near-infrared EBL
spectrum can be detected tomographically out to $z\sim 6$. We also predict a
high-significance measurement ($\sim 10^2$-$10^4\sigma$) of the small-scale
cross-power spectrum out to $z\sim 10$. The amplitudes of the large-scale cross
power spectra can constrain the cosmic evolution of the stellar synthesis
process through both continuum and the line emission, while on the nonlinear
and Poisson noise scales, the high-sensitivity measurements can probe the mean
spectra associated with the tracer population across redshift.
