  While it is difficult to observe the first black hole seeds in the early
Universe, we can study intermediate mass black holes (IMBHs) in local dwarf
galaxies for clues about their origins. In this paper we present a sample of
variability--selected AGN in dwarf galaxies using optical photometry from the
Zwicky Transient Facility (ZTF) and forward--modeled mid--IR photometry of
time--resolved Wide--field Infrared Survey Explorer ({\it WISE}) coadded
images. We found that 44 out of 25,714 dwarf galaxies had optically variable
AGN candidates, and 148 out of 79,879 dwarf galaxies had mid--IR variable AGN
candidates, corresponding to active fractions of $0.17\pm0.03$\% and
$0.19\pm0.02$\% respectively. We found that spectroscopic approaches to AGN
identification would have missed 81\% of our ZTF IMBH candidates and 69\% of
our {\it WISE} IMBH candidates. Only $9$ candidates have been detected
previously in radio, X-ray, and variability searches for dwarf galaxy AGN. The
ZTF and {\it WISE} dwarf galaxy AGN with broad Balmer lines have virial masses
down to $10^{5.5}M_\odot$ and for the rest of the sample, BH masses predicted
from host galaxy mass range between
$10^{5.2}M_\odot<M_{\text{BH}}<10^{7.3}M_\odot$. We found that only 5 of 152
previously reported variability--selected AGN candidates from the Palomar
Transient Factory in common with our parent sample were variable in ZTF. We
also determined a nuclear supernova fraction of $0.05\pm0.01$\% year$^{-1}$ for
dwarf galaxies in ZTF. Our ZTF and {\it WISE} IMBH candidates show the promise
of variability searches for the discovery of otherwise hidden low mass AGN.
