We investigate how topological defects influence the excitonic behavior in (6,5) semiconducting single-walled carbon nanotubes. Our theoretical study demonstrates that topological defects, particularly the widely occurring Stone-Wales defect, can act as efficient traps for triplet excitons, characterized by significant zero-field splitting consistent with experimental data and a small singlet-triplet energy gap. Additionally, the weak electron-phonon coupling positions these defects as promising candidates for single-photon emission at telecom wavelengths (1.6 μm). These findings pave the way for enhancing the performance of carbon nanotube-based quantum light sources and optoelectronic devices.