  In December 2018, the main-belt asteroid (6478)~Gault was reported to display
activity. Gault is an asteroid belonging to the Phocaea dynamical family and
was not previously known to be active, nor was any other member of the Phocaea
family. In this work we present the results of photometric and spectroscopic
observations that commenced soon after the discovery of activity. We obtained
observations over two apparitions to monitor its activity, rotation period,
composition, and possible non-gravitational orbital evolution. We find that
Gault has a rotation period of $P = 2.4929 \pm 0.0003$ hours with a lightcurve
amplitude of $0.06$ magnitude. This short rotation period close to the spin
barrier limit is consistent with Gault having a density no smaller than $\rho =
1.85$~g/cm$^3$ and its activity being triggered by the YORP spin-up mechanism.
Analysis of the Gault phase curve over phase angles ranging from $0.4^{\circ}$
to $23.6^{\circ}$ provides an absolute magnitude of $H = 14.81 \pm 0.04$,
$G1=0.25 \pm 0.07$, and $G2= 0.38 \pm 0.04$. Model fits to the phase curve find
the surface regolith grain size constrained between 100-500 $\rm{\mu}$m. Using
relations between the phase curve and albedo we determine that the geometrical
albedo of Gault is $p_{\rm v} = 0.26 \pm 0.05$ corresponding to an equivalent
diameter of $D = 2.8^{+0.4}_{-0.2}$ km. Our spectroscopic observations are all
consistent with an ordinary chondrite-like composition (S, or Q-type in the
Bus-DeMeo taxonomic classification). A search through archival photographic
plate surveys found previously unidentified detections of Gault dating back to
1957 and 1958. Only the latter had been digitized, which we measured to nearly
double the observation arc of Gault. Finally, we did not find any signal of
activity during the 2020 apparition or non-gravitational effects on its orbit.
