CAPOS: The bulge Cluster APOgee Survey III. Spectroscopic Tomography of Tonantzintla 2

(ABRIDGED) We have performed the first detailed spectral analysis of red giant members of the relatively high-metallicity globular cluster (GC) Tononzintla~2 (Ton~2) using high-resolution near-infrared spectra collected with the Apache Point Observatory Galactic Evolution Experiment II survey (APOGEE-2), obtained as part of the bulge Cluster APOgee Survey. We investigate chemical abundances for a variety of species including the light-, odd-Z, $\alpha$-, Fe-peak, and neutron-capture elements from high S/N spectra of seven giant members. The derived mean cluster metallicity is [Fe/H]$=-0.70\pm0.05$, with no evidence for an intrinsic metallicity spread. Ton~2 exhibits a typical $\alpha$-enrichment that follows the trend for high-metallicity Galactic GCs, similar to that seen in 47~Tucanae and NGC~6380. We find a significant nitrogen spread ($>0.87$ dex), and a large fraction of nitrogen-enriched stars that populate the cluster. Given the relatively high-metallicity of Ton~2, these nitrogen-enriched stars are well above the typical Galactic levels, indicating the prevalence of the multiple-population phenomenon in this cluster which also contains several stars with typical low, first-generation N abundances. We also identify the presence of [Ce/Fe] abundance spread in Ton~2, which is correlated with the nitrogen enhancement, indicating that the \textit{s}-process enrichment in this cluster has been produced likely by relatively low-mass Asymptotic Giant Branch stars. Furthermore, we find a mean radial velocity of the cluster, $-178.6\pm0.86$ km s$^{-1}$ with a small velocity dispersion, 2.99$\pm$0.61 km s$^{-1}$, which is typical of a GC. We also find a prograde bulge-like orbit for Ton~2 that appears to be radial and highly eccentric.