We present a new insight into the absolute two-plasmon decay (TPD) instability in nonuniform plasmas by identifying the resonance density range as the key parameter governing the growth of the resonant absolute modes. This range is defined as the density interval within which these resonant modes still exhibit growth in homogeneous plasmas. This range properly characterizes the spatial growth region of the resonant absolute modes in a series of linear fluid simulations across broad parameter spaces. Building on this insight, we investigate the absolute growth of TPD modes driven by laser pulses with intensity modulations, a common feature in broadband lasers used to suppress laser plasma instabilities. We establish the relationship between the resonance density range and the threshold time interval between intensity peaks, beyond which absolute growth is suppressed.