  We present a comprehensive study of the nonproportionality of NaI(Tl)
scintillation detectors within the context of dark matter search experiments.
Our investigation, which integrates COSINE-100 data with supplementary $\gamma$
spectroscopy, measures light yields across diverse energy levels from
full-energy $\gamma$ peaks produced by the decays of various isotopes. These
$\gamma$ peaks of interest were produced by decays supported by both long and
short-lived isotopes. Analyzing peaks from decays supported only by short-lived
isotopes presented a unique challenge due to their limited statistics and
overlapping energies, which was overcome by long-term data collection and a
time-dependent analysis. A key achievement is the direct measurement of the
0.87 keV light yield, resulting from the cascade following electron capture
decay of $^{22}$Na from internal contamination. This measurement, previously
accessible only indirectly, deepens our understanding of NaI(Tl) scintillator
behavior in the region of interest for dark matter searches. This study holds
substantial implications for background modeling and the interpretation of dark
matter signals in NaI(Tl) experiments.
