In this work, a Thai disability labor employment model was developed using a nonlinear delay-differential equation, with the delay term capturing policy implementation lags arising from administrative processes. In addition, we established theoretical results that guarantee the existence of equilibria and characterized the effect of implementation delays on long-term market stability. In particular, the global asymptotic stability under sufficient conditions was proved using a Lyapunov approach. To evaluate parameter influence, a normalized sensitivity analysis was conducted to identify the most significant factors for unemployment dynamics. Finally, numerical results were demonstrated in two stages. First, the numerical experiments were performed to validate the theoretical stability results. Second, the model parameters were estimated using historical Thai data for 2022–2025. To improve the model's consistency with observed data, the vacancy dynamics were refined by introducing additional variables. The proposed model provides a quantitative tool for analyzing policy delays and designing effective intervention strategies in the disability labor market.