  Next-generation megawatt-scale neutrino beams open the way to studying
neutrino-nucleus scattering resorting, for the first time, to gaseous targets.
This could lead to deeper knowledge of neutrino cross sections in the energy
region between hundreds of MeV and a few GeV, of interest for the upcoming
generation of long-baseline neutrino oscillation experiments. The challenge is,
therefore, to accurately track and (especially) time the particles produced in
neutrino interactions in large and seamless volumes down to few-MeV energies.
We propose to accomplish this through an optically-read time projection chamber
(TPC) filled with high-pressure argon and equipped with both tracking and
timing functions. In this work, we present a detailed study of the time-tagging
capabilities of such a device, based on end-to-end optical simulations that
include the effect of photon propagation, photosensor response, dark-count rate
and pulse reconstruction. We show that the neutrino interaction time could be
reconstructed from the primary-scintillation signal with a precision in the
range 1--2.5~ns ($\sigma$) for point-like deposits with energies down to 5~MeV,
and well below 1~ns for minimum-ionizing particle tracks. A discussion on
previous limitations towards such a detection technology, and how they can be
realistically overcome in the near future thanks to recent developments in the
field, is presented (particularly the strong scintillation yields recently
reported for Ar/CF$_4$ mixtures). The performance presented in our analysis
seems to be well within reach of next-generation neutrino-oscillation
experiments through the instrumentation of the proposed TPC with conventional
reflective materials and a SiPM carpet behind a transparent cathode.
