We present excitation-pulse-width- and pump-power-dependent microelectroluminescence and photon statistics measurements on electrically driven single-photon devices based on InP/AlGaInP quantum dots (QDs). For an excitation regime far below QD saturation, the results show a characteristic decrease of the purity of the single-photon emission [${g}^{(2)}(0)$ value] with increasing excitation pulse width. For stronger excitation pulses close to QD saturation, strong antibunching is maintained for a much larger pulse width. In this case the ground-state exciton emission, which is used for the single-photon source, is inhibited during the pump pulse due to the presence of higher excited states. This prevents multiple-ground-state emission and reexcitation during long pump pulses and delays the single-photon emission to the end of the pulse, as predicted by theory and confirmed experimentally.