The temporal afterglow between two pulses of a repetitively pulsed radio-frequency driven low-pressure argon-acetylene plasma is experimentally explored using laser-induced photodetachment combined with microwave cavity resonance spectroscopy. The densities of electrons and negatively charged species, i.e., anions and dust particles, are measured temporally resolved until 1.9 s in the temporal plasma afterglow. Two different plasma-on times are adjusted to investigate the dynamics of anions and dust particles in the afterglow phase. The measurements show that while electrons decay rapidly within the first few milliseconds of the afterglow phase, the negatively charged species reside much longer in the plasma after the plasma is switched off. The electron density decay is measured to be faster for a longer plasma-on time. This effect is attributed to an enhanced recombination rate due to a higher dust particle density and/or size. The density of negatively charged species decays within two different timescales. The first 20 milliseconds of the afterglow is marked with a rapid decay in the negatively charged species density, in contrast with their slow density decay in the second time scale. Moreover, a residual of the negatively charged species densities is detected as long as 1.9 s after extinguishing the plasma.