  Thirteen dwarf galaxies have recently been found to host radio-selected
accreting massive black hole (MBH) candidates, some of which are ``wandering"
in the outskirts of their hosts. We present 9 GHz Very Long Baseline Array
(VLBA) observations of these sources at milliarcsecond resolution. Our
observations have beam solid angles ${\sim}10^4$ times smaller than the
previous Very Large Array (VLA) observations at 9 GHz, with comparable point
source sensitivities. We detect milliarcsecond-scale radio sources at the
positions of the four VLA sources most distant from the photo-centers of their
associated dwarf galaxies. These sources have brightness temperatures of
${>}10^6~\mathrm{K}$, consistent with active galactic nuclei (AGNs), but the
significance of their preferential location at large distances
($p$-value~$=0.0014$) favors a background AGN interpretation. The VLBA
non-detections toward the other 9 galaxies indicate that the VLA sources are
resolved out on scales of tens of milliarcseconds, requiring extended radio
emission and lower brightness temperatures consistent with either star
formation or radio lobes associated with AGN activity. We explore the star
formation explanation by calculating the expected radio emission for these nine
VLBA non-detections, finding that about 5 have VLA luminosities that are
inconsistent with this scenario. Of the remaining four, two are associated with
spectroscopically confirmed AGNs that are consistent with being located at
their galaxy photo-centers. There are therefore between 5 and 7 wandering MBH
candidates out of the 13 galaxies we observed, although we cannot rule out
background AGNs for five of them with the data in hand.
