Time-resolved number densities of N2(A3Σu+,v=0,1) molecules in diffuse ns pulse discharge plasmas in N2, N2-H2, N2-CH4, N2-CO2, and N2-CO2-CH4 are measured by Tunable Diode Laser Absorption Spectroscopy (TDLAS). The first series of measurements is made in the discharge pulse bursts at a relatively low pulse repetition rate (3 kHz), when the N2(A3Σu+) generation and decay after individual discharge pulses is fully resolved. The second set of data is taken during a sequence of two pulse bursts generated at a higher pulse repetition rate (100 kHz), for different delay times between the first and second bursts. This approach is used to determine the effect of accumulation and decay of reacting species generated in the plasma, including N, H, and O atoms, CO molecules, and C2 hydrocarbon product species, on the rate of N2(A3Σu+) production and quenching. The effect of these species can be isolated since the rates of N2(A3Σu+) quenching by the initial reactant species (H2, CH4, and CO2) are slow. Comparison of the measurement results with the kinetic modeling predictions is used to obtain insight into the plasma chemical reaction kinetics. The results complement the measurements of N, H, O, and CO in high-pressure reacting plasmas, and help quantify the plasma chemical processes driven by the electron impact dissociation, electronic excitation, and reactive quenching of the excited electronic states. The present results may be used for the development and validation of higher fidelity kinetic models of reacting plasmas, incorporating state-specific electronic and vibrational energy transfer and chemical reactions.