  The view of globular clusters (GCs) as simple systems continues to unravel,
revealing complex objects hosting multiple chemical peculiarities. Using
differential abundance analysis, we probe the chemistry of the Type I GC, NGC
288 and the Type II GC, NGC 362 at the 2\% level for the first time. We measure
20 elements and find differential measurement uncertainties on the order
0.01-0.02 dex in both clusters. The smallest uncertainties are measured for Fe
I in both clusters, with an average uncertainty of $\sim$0.013 dex. Dispersion
in the abundances of Na, Al, Ti I, Ni, Fe I, Y, Zr, Ba and Nd are recovered in
NGC 288, none of which can be explained by a spread in He. This is the first
time, to our knowledge, a statistically significant spread in $s$-process
elements and a potential spread in metallicity has been detected in NGC 288. In
NGC 362, we find significant dispersion in the same elements as NGC 288, with
the addition of Co, Cu, Zn, Sr, La, Ce, and Eu. Two distinct groups are
recovered in NGC 362, separated by 0.3 dex in average differential $s$-process
abundances. Given strong correlations between Al and several $s$-process
elements, and a significant correlation between Mg and Si, we propose that the
$s$-process rich group is younger. This agrees with asymptotic giant branch
star (AGB) enrichment between generations, if there is overlap between low- and
intermediate-mass AGBs. In our scenario, the older population is dominated by
the $r$-process with a $\Delta^{\mathrm{La}}-\Delta^{\mathrm{Eu}}$ ratio of
$-0.16\pm0.06$. We propose that the $r$-process dominance and dispersion found
in NGC 362 are primordial.
