  DG Tau A, a class-II young stellar object (YSO) displays both thermal, and
non-thermal, radio emission associated with its bipolar jet. To investigate the
nature of this emission, we present sensitive ($\sigma\sim2\,\mu {\rm Jy
\,beam^{-1}}$), Karl G.\ Jansky Very Large Array (VLA) $6$ and $10\,{\rm GHz}$
observations. Over $3.81\,{\rm yr}$, no proper motion is observed towards the
non-thermal radio knot C, previously thought to be a bowshock. Its quasi-static
nature, spatially-resolved variability and offset from the central jet axis
supports a scenario whereby it is instead a stationary shock driven into the
surrounding medium by the jet. Towards the internal working surface, knot A, we
derive an inclination-corrected, absolute velocity of $258\pm23\, {\rm
km\,s^{-1}}$. DG Tau A's receding counterjet displays a spatially-resolved
increase in flux density, indicating a variable mass loss event, the first time
such an event has been observed in the counterjet. For this ejection, we
measure an ionised mass loss rate of $(3.7\pm1.0) \times 10^{-8}\, {\rm
M_\odot\, yr^{-1}}$ during the event. A contemporaneous ejection in the
approaching jet isn't seen, showing it to be an asymmetric process. Finally,
using radiative transfer modelling, we find that the extent of the radio
emission can only be explained with the presence of shocks, and therefore
reionisation, in the flow. Our modelling highlights the need to consider the
relative angular size of optically thick, and thin, radio emission from a jet,
to the synthesised beam, when deriving its physical conditions from its
spectral index.
