In single-walled carbon nanotubes, electron-hole pairs form tightly bound excitons because of limited screening. These excitons display a variety of interactions and processes that could be exploited for applications in nanoscale photonics and optoelectronics. Here we report on optical pulse-train generation from individual air-suspended carbon nanotubes under an application of square-wave gate voltages. Electrostatically induced carrier accumulation quenches photoluminescence, while a voltage sign reversal purges those carriers, resetting the nanotubes to become luminescent temporarily. Frequency-domain measurements reveal photoluminescence recovery with characteristic frequencies that increase with excitation laser power, showing that photoexcited carriers provide a self-limiting mechanism for pulsed emission. Time-resolved measurements directly confirm the presence of an optical pulse train synchronized to the gate voltage signal, and flexible control over pulse timing and duration is also demonstrated. These results identify an unconventional route for optical pulse generation and electrical-to-optical signal conversion, opening up new prospects for controlling light at the nanoscale.