A mixed composition of light-to-heavy nuclei elements ($^1$H, $^4$He, $^{14}$N, $^{28}$Si, $^{56}$Fe) at injection fits the ultrahigh-energy cosmic ray (UHECR; $E>10^{17}$ eV) spectrum data measured by the Pierre Auger Observatory, beyond the ankle, i.e., $E\gtrsim 5\times10^{18}$ eV. However, the composition fit can be further improved by the addition of light nuclei at the highest energies. We consider the light nuclei to originate from a discrete source population consisting of protons ($^{1}$H). We constrain the maximum allowed proton fraction at the highest-energy bin at $3.5\sigma$ statistical significance. Including the redshift evolution of sources as a free parameter further improves the composition fit. We find that low-luminosity gamma-ray bursts match the best-fit evolution index in the case of the one-population model. Active galactic nuclei are the plausible candidates for light nuclei injection in the two-population model, whereas tidal disruption events can inject heavy nuclei composition. We also present the secondary neutrino flux in one- and two-population models, constraining the composition at highest energies.