  Swift J1858.6-0814 is a transient neutron star X-ray binary discovered in
October 2018. Multi-wavelength follow-up observations across the
electromagnetic spectrum revealed many interesting properties, such as erratic
flaring on minute timescales and evidence for wind outflows at both X-ray and
optical wavelengths, strong and variable local absorption, and an anomalously
hard X-ray spectrum. Here, we report on a detailed radio observing campaign
consisting of one observation at 5.5/9 GHz with the Australia Telescope Compact
Array, and nine observations at 4.5/7.5 GHz with the Karl G. Jansky Very Large
Array. A radio counterpart with a flat to inverted radio spectrum is detected
in all observations, consistent with a compact jet being launched from the
system. Swift J1858.6-0814 is highly variable at radio wavelengths in most
observations, showing significant variability when imaged on 3-to-5-minute
timescales and changing up to factors of 8 within 20 minutes. The periods of
brightest radio emission are not associated with steep radio spectra, implying
they do not originate from the launching of discrete ejecta. We find that the
radio variability is similarly unlikely to have a geometric origin, be due to
scintillation, or be causally related to the observed X-ray flaring. Instead,
we find that it is consistent with being driven by variations in the accretion
flow propagating down the compact jet. We compare the radio properties of Swift
J1858.6-0814 with those of Eddington-limited X-ray binaries with similar X-ray
and optical characteristics, but fail to find a match in radio variability,
spectrum, and luminosity.
