  The fraction of low-mass galaxies hosting an intermediate-mass black hole
(IMBH, with masses $M_{\rm BH} \approx 10^2-10^5$ M$_\odot$), is sensitive to
how black hole seeds formed in the early Universe but is observationally still
unconstrained. In this paper, we assemble a sample of dwarf galaxies within 10
Mpc hosting bright nuclear star clusters (NSCs) that could host IMBHs. For a
subset of them, we use their observed surface brightness from {\it Hubble Space
Telescope} (\hst) images, an assumed synthetic spectrum of their stellar
population, Jeans Anisotropic Model (JAM) of the stellar dynamics, and the {\tt
HSIM} simulator software to create mock observations with the High Angular
Resolution Monolithic Optical and Near-infrared Integral (HARMONI) field
spectrograph for the Extremely Large Telescope (ELT). We analyze the simulated
data cube like real data, using JAM to infer the IMBH mass and its error in a
Bayesian framework. Our simulations show that the ELT/HARMONI instrument can
clearly detect the existence of IMBH demographics in NSCs down to a mass of
about 0.5\% of the NSC.
