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Active galactic nuclei (AGNs) in dwarf galaxies (dwarf AGNs) are believed to host accreting intermediate-mass black holes (IMBHs). The demographics of dwarf AGNs are an important tracer of supermassive black hole (SMBH) growth, because their relic IMBHs act as a fossil record of SMBH seeding pathways at high redshift. Being ubiquitous across wavelengths and timescales, variability is useful for AGN identification and is an important probe of BH accretion. The first part of this dissertation is focused on observational evidence for a characteristic thermal timescale in accretion disks using optical light curves from stellar-mass accreting systems to SMBHs in AGNs. This was motivated by our discovery of ~days timescale variability in the optical light curve of the well-known dwarf AGN NGC 4395. I will then discuss my work selecting dwarf AGNs from variability beyond z ~ 0.1 (the limit of what has been probed by previous work) using light curves from the Dark Energy Survey supernova survey program. I will presents a phenomenological forward model for forecasting dwarf AGNs and constraining the corresponding IMBH number density with variability. I will present my work on spectroscopic tests of IMBHs in extremely metal-poor galaxies. Finally, I will discuss future endeavors with current and upcoming facilities as we begin to establish IMBHs as unique probes of BH accretion and tracers of SMBH seeding and growth.