  We present a methodology for modeling the joint ionizing impact due to a
"simple X-ray population" (SXP) and its corresponding simple stellar population
(SSP), where "simple" refers to a single age and metallicity population. We
construct composite spectral energy distributions (SEDs) including
contributions from ultra-luminous X-ray sources (ULXs) and stars, with
physically meaningful and consistent consideration of the relative
contributions of each component as a function of instantaneous burst age and
stellar metallicity. These composite SEDs are used as input for photoionization
modeling with Cloudy, from which we produce a grid for the time- and
metallicity-dependent nebular emission from these composite populations. We
make the results from the photoionization simulations publicly available. We
find that the addition of the SXP prolongs the high-energy ionizing output from
the population, and correspondingly increases the intensity of nebular lines
such as He II $\lambda$1640,4686, [Ne V] $\lambda$3426,14.3$\mu$m, and [O IV]
25.9$\mu$m by factors of at least two relative to models without an SXP
spectral component. This effect is most pronounced for instantaneous bursts of
star formation on timescales $>$ 10 Myr and at low metallicities ($\sim$ 0.1
$Z_{\odot}$), due to the imposed time- and metallicity-dependent behavior of
the SXP relative to the SSP. We propose nebular emission line diagnostics
accessible with JWST suitable for inferring the presence of a composite SXP +
SSP, and discuss how the ionization signatures compare to models for sources
such as intermediate mass black holes.
