  Dwarf galaxies are promising test beds for constraining models of
supermassive and intermediate-mass black holes (MBH) via their black hole
occupation fraction (BHOF). Disentangling seeding from the confounding effects
of mass assembly over a Hubble time is a challenging problem, that we tackle in
this study with a suite of semi-analytical models (SAMs). We show how measured
BHOF depends on the lowest black hole mass or AGN luminosity achieved by a
survey. To tell seeding models apart, we need to detect or model all AGN
brighter than $10^{37}\ \rm{erg \ s^{-1}}$ in galaxies of $M_* \sim 10^{8-10} \
\rm{M_{\odot}}$. Shallower surveys, like eRASS, cannot distinguish between seed
models even with the compensation of a much larger survey volume. We show that
the AMUSE survey, with its inference of the MBH population underlying the
observed AGN, strongly favors heavy seed models, growing with either a
power-law Eddington Ratio Distribution Function (ERDF) or one in which black
hole accretion is tagged to the star-formation rate (AGN-MS). These two growth
channels can then be distinguished by the AGN luminosity function at $>
10^{40}\ \rm{erg \ s^{-1}}$, with the AGN-MS model requiring more accretion
than observed at z $\sim$ 0. Thus, current X-ray observations favour heavy
seeds whose Eddington ratios follow a power-law distribution. The different
models also predict different radio scaling relations, which we quantify using
the fundamental plane of black hole activity. We close with recommendations for
the design of upcoming multi-wavelength campaigns that can optimally detect
MBHs in dwarf galaxies.
