  The ultra-faint dwarf galaxy Reticulum~II was enriched by a single rare and
prolific r-process event. The r-process content of Reticulum~II thus provides a
unique opportunity to study metal mixing in a relic first galaxy. Using
multi-object high-resolution spectroscopy with VLT/GIRAFFE and Magellan/M2FS,
we identify 32 clear spectroscopic member stars and measure abundances of Mg,
Ca, Fe, and Ba where possible. We find $72^{+10}_{-12}$% of the stars are
r-process-enhanced, with a mean
$\left\langle\mbox{[Ba/H]}\right\rangle=-1.68~\pm~0.07$ and unresolved
intrinsic dispersion $\sigma_{\rm [Ba/H]} < 0.20$. The homogeneous r-process
abundances imply that Ret~II's metals are well-mixed by the time the r-enhanced
stars form, which simulations have shown requires at least 100 Myr of metal
mixing in between bursts of star formation to homogenize. This is the first
direct evidence of bursty star formation in an ultra-faint dwarf galaxy. The
homogeneous dilution prefers a prompt and high-yield r-process site, such as
collapsar disk winds or prompt neutron star mergers. We also find evidence from
[Ba/H] and [Mg/Ca] that the r-enhanced stars in Ret~II formed in the absence of
substantial pristine gas accretion, perhaps indicating that ${\approx}70$% of
Ret~II stars formed after reionization.
